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CBSE Class 10 Maths Case Study Questions for Chapter 9 - Some Applications of Trigonometry (Published By CBSE)

Check case study questions for cbse class 10 maths chapter 9 - some applications of trigonometry. these questions are published by the cbse itself for class 10 students..

Gurmeet Kaur

Case study based questions are new for class 10 students. Therefore, it is quite essential that students practice with more of such questions so that they do not have problem in solving them in their Maths board exam. We have provided here the case study questions for CBSE Class 10 Maths Chapter 9 - Some Applications of Trigonometry. All these questions have been published by the Central Board of Secondary Education (CBSE) for the class 10 students. Therefore, students must solve all the questions seriously so that they may score the desired marks in their Maths exam.

Check Case Study Questions for Class 10 Maths Chapter 9:

CASE STUDY 1:

A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919. The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 metres) in height.

applications of trigonometry case study questions

1. What is the angle of elevation if they are standing at a distance of 42m away from the monument?

Answer: b) 45 o

2. They want to see the tower at an angle of 60 o . So, they want to know the distance where they should stand and hence find the distance.

Answer: a) 25.24 m

3. If the altitude of the Sun is at 60 o , then the height of the vertical tower that will cast a shadow of length 20 m is

a) 20√3 m

b) 20/ √3 m

c) 15/ √3 m

d) 15√3 m

Answer: a) 20√3 m

4. The ratio of the length of a rod and its shadow is 1:1. The angle of elevation of the Sun is

5. The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is

a) corresponding angle

b) angle of elevation

c) angle of depression

d) complete angle

Answer: a) corresponding angle

CASE STUDY 2:

A Satellite flying at height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka, them being Nanda Devi(height 7,816m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite, to the top of Nanda Devi and Mullayanagiri are 30° and 60° respectively. If the distance between the peaks of the two mountains is 1937 km, and the satellite is vertically above the midpoint of the distance between the two mountains.

applications of trigonometry case study questions

1. The distance of the satellite from the top of Nanda Devi is

a) 1139.4 km

b) 577.52 km

d) 1025.36 km

Answer: a) 1139.4 km

2. The distance of the satellite from the top of Mullayanagiri is

Answer: c) 1937 km

3. The distance of the satellite from the ground is

Answer: b) 577.52 km

4. What is the angle of elevation if a man is standing at a distance of 7816m from Nanda Devi?

5.If a mile stone very far away from, makes 45 o to the top of Mullanyangiri mountain. So, find the distance of this mile stone from the mountain.

a) 1118.327 km

b) 566.976 km

Also Check:

Case Study Questions for All Chapters of CBSE Class 10 Maths

Tips to Solve Case Study Based Questions Accurately

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Case Study Questions for Class 10 Maths Chapter 9 Applications of Trigonometry

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies as well. In that, a paragraph will be given, and then the MCQ questions or subjective questions based on it will be asked.

Here, we have provided case based/passage-based questions for Class 10 Maths Chapter 9 Applications of Trigonometry

Case Study Questions:

Question 1:

A Satellite flying at height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka, them being Nanda Devi (height 7,816m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite to the top of Nanda Devi and Mullayanagiri are 30° and 60° respectively. If the distance between the peaks of two mountains is 1937 km, and the satellite is vertically above the midpoint of the distance between the two mountains.

applications of trigonometry case study questions

(i) The distance of the satellite from the top of Mullayanagiri is

(a) 1139.4 km

(b) 577.52 km

(c) 1937 km

(d) 1025.36 km

(ii) If a mile stone very far away from, makes 45 to the top of Mullanyangiri mountain. So, find the distance of this milestone form the mountain.

(a) 1118.327 km

(b) 566.976 km

(iii) The distance of the satellite from the ground is

(iv) The distance of the satellite from the top of Nanda Devi is

(v) What is the angle of elevation if a man is standing at a distance of 7816m from Nanda Devi?

Question 2:

A group of students of class X visited India Gate on an educational trip. The teacher and students had interest in history as well. The teacher narrated that India Gate, official name Delhi Memorial, originally called All-India War Memorial, monumental sandstone arch in New Delhi, dedicated to the troops of British India who died in wars fought between 1914 and 1919.The teacher also said that India Gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway), is about 138 feet (42 m) in height.

applications of trigonometry case study questions

(i) What is the angle of elevation if they are standing at a distance of 42 m away from the monument? (a) 30° (b) 45° (c) 60° (d) 0°

(ii) They want to see the tower at an angle of 60°. So, they want to know the distance where they should stand and hence find the distance. (a) 25.24 m (b) 20.12 m (c) 42 m (d) 24.24 m

(iii) If the altitude of the Sun is at 60°, then the height of the vertical tower that will cast a shadow of length 20 m is (a) 20 √ 3 m (b) 20/ √ 3 m (c) 15/ √ 3 m (d) 15 √ 3 m

(iv) The ratio of the length of a rod and its shadow is 1 : 1. The angle of elevation of the Sun is (a) 30° (b) 45° (c) 60° (d) 90°

(v) The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is (a) corresponding angle (b) angle of elevation (c) angle of depression (d) complete angle

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Chapter 1 Real Numbers Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables C hapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Some Applications of Trigonometry Chapter 10 Circles Chapter 11 Constructions Chapter 12 Areas Related to Circles Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability

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Case Study on Some Applications of Trigonometry Class 10 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Some Applications of Trigonometry Class 10 Maths can use this page to download the PDF file. 

The case study questions on Some Applications of Trigonometry are based on the CBSE Class 10 Maths Syllabus, and therefore, referring to the Some Applications of Trigonometry case study questions enable students to gain the appropriate knowledge and prepare better for the Class 10 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Some Applications of Trigonometry Class 10 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Some Applications of Trigonometry, therefore, they prepared a set of solutions along with the case study questions on Some Applications of Trigonometry.

The case study on Some Applications of Trigonometry Class 10 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Some Applications of Trigonometry case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Some Applications of Trigonometry Case Study Questions on Class 10 Maths?

There are three major reasons why one should solve Some Applications of Trigonometry case study questions on Class 10 Maths - all those major reasons are discussed below:

  • To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 10 Maths students, therefore, it is important to solve Some Applications of Trigonometry Case study questions as it will help better prepare for the Class 10 board exam preparation.
  • Develop Problem-Solving Skills: Class 10 Maths Some Applications of Trigonometry case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 10 students develop their problem-solving skills, which are essential for success in any profession rather than Class 10 board exam preparation.
  • Understand Real-Life Applications: Several Some Applications of Trigonometry Class 10 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Some Applications of Trigonometry as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Some Applications of Trigonometry?

Students can choose their own way to answer Case Study on Some Applications of Trigonometry Class 10 Maths, however, we believe following these three steps would help a lot in answering Class 10 Maths Some Applications of Trigonometry Case Study questions.

  • Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
  • Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Some Applications of Trigonometry questions quickly.
  • Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Some Applications of Trigonometry Class 10 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 10 Some Applications of Trigonometry?

 A few essential things to know to solve Case Study Questions on Class 10 Some Applications of Trigonometry are -

  • Basic Formulas of Some Applications of Trigonometry: One of the most important things to know to solve Case Study Questions on Class 10 Some Applications of Trigonometry is to learn about the basic formulas or revise them before solving the case-based questions on Some Applications of Trigonometry.
  • To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 10 Maths Some Applications of Trigonometry case study questions.
  • Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

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Class 10 Maths: Case Study Questions of Chapter 9 Some Applications of Trigonometry PDF

Case study Questions on the Class 10 Mathematics Chapter 9  are very important to solve for your exam. Class 10 Maths Chapter 9 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 10 Maths Chapter 9 Some Applications of Trigonometry

applications of trigonometry case study questions

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Some Applications of Trigonometry Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 9 Some Applications of Trigonometry

Case Study/Passage Based Questions

There are two temples on each bank of a river. One temple is 50 m high. A man, who is standing on the top of a 50 m high temple, observed from the top that the angle of depression of the top and foot of other temples are 30° and 60° respectively.

applications of trigonometry case study questions

The measure of ∠ADF is equal to (a) 45° (b) 60° (c) 30° (d) 90°

Answer: (c) 30°

A measure of ∠ACB is equal to (a) 45° (b) 60° (c) 30° (d) 90°

Answer: (b) 60°

Width of the river is (a) 28.90 m (b) 26.75 m (c) 25 m (d) 27 m

Answer: (a) 28.90 m

The height of the other temple is (a) 32.5 m (b) 35 m (c) 33.33 m (d) 40 m

Answer: (c) 33.33 m

The angle of depression is always (a) reflex angle (b) straight (c) an obtuse angle (d) an acute angle

Answer: (d) an acute angle

Rohit is standing at the top of the building observes a car at an angle of 30°, which is approaching the foot of the building at a uniform speed. 6 seconds later, the angle of depression of the car formed to be 60°, whose distance at that instant from the building is 25 m.

applications of trigonometry case study questions

The height of the building is (a) 25√2 m (b) 50 m (c) 25√3 m (d) 25 m

Answer: (c) 25√3 m

Distance between two positions of the car is (a) 40 m (b) 50 m (c) 60 m (d) 75 m

Answer: (b) 50 m

Total time is taken by the car to reach the foot of the building from the starting point is (a) 4 secs (b) 3 secs (c) 6 secs (d) 9 secs

Answer: (d) 9 secs

The distance of the observer from the car when it makes an angle of 60° is (a) 25 m (b) 45 m (c) 50 m (d) 75 m

Answer: (c) 50 m

The angle of elevation increases (a) when point of observation moves towards the object (b) when point of observation moves away from the object (c) when object moves away from the observer (d) None of these

Answer: (a) when point of observation moves towards the object

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 9 Some Applications of Trigonometry with Answers Pdf free download has been useful to an extent. If you have any other queries of CBSE Class 10 Maths Some Applications of Trigonometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Case study questions class 10 maths chapter 9 applications of trigonometry cbse board term 2.

Case Study Questions Class 10 Maths Chapter 9 Applications of Trigonometry CBSE Board Term 2

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Unit 9: Some applications of Trigonometry

Applications of trigonometry 9.1.

  • Intro to heights and distances (Opens a modal)
  • Heights and distances word problem: distance between two buildings (Opens a modal)
  • Heights and distances word problem: height of a cloud above a lake (Opens a modal)
  • Word problems: one triangle involved Get 3 of 4 questions to level up!
  • Word problems: two triangles involved Get 3 of 4 questions to level up!
  • Some applications of Trigonometry 9.1 Get 7 of 10 questions to level up!

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Case Study Questions Class 10 Maths Some Applications of Trigonometry

Case study questions class 10 maths chapter 9 some applications of trigonometry.

CBSE Class 10 Case Study Questions Maths Some Applications of Trigonometry. Term 2 Important Case Study Questions for Class 10 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Some Applications of Trigonometry.

At Case Study Questions there will given a Paragraph. In where some Important Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks, 4 marks.

CBSE Case Study Questions Class 10 Maths Some Applications of Trigonometry

Case Study – 1

A group of students of class X visited India gate on an education trip the teacher and students had interested in history as well. the narrate the India gate. Official name Delhi Memorial originally called All- India War Memorial, monumental sand stone arch in new Delhi dedicated to the troops of British India who died in wars fought between 1914 and 1919. The teacher also said that india gate, which is located at the eastern end of the Rajpath (formerly called the Kingsway) is about 138 feet (42 metres) in height.

[KVS Raipur 2021 – 22]

applications of trigonometry case study questions

(i) if the altitude of the sun is at 600. then the height of the vertical tower that will cast a shadow of length 20 m is ?

applications of trigonometry case study questions

Answer – 20√3m

(ii) The ratio of the length of a Rod and its shadow is 1:1. The angle of elevation of the sun is?

Answer – 45 0

(iii) The angle formed by the line of sight with the horizontal when the object viewed is below the horizontal level is

  • a) corresponding angle
  • b) angle of elevation
  • c) angle of depression
  • d) complete angle

Answer – a) corresponding angle 

iv) What is the angle of elevation if they are standing at a distance of 42m away from the monument?

Answer – b) 45 0

CASE STUDY 2:

A Satellite flying at height h is watching the top of the two tallest mountains in Uttarakhand and Karnataka ,them being Nanda Devi (height 7,816m) and Mullayanagiri (height 1,930 m). The angles of depression from the satellite , to the top of Nanda Devi and Mullayanagiri are 30° and 60° respectively. If the distance between the peaks of two mountains is 1937 km , and the satellite is vertically above the midpoint of the distance between the two mountains.

[ CBSE Academic Question Paper ]

applications of trigonometry case study questions

(1) The distance of the satellite from the top of Mullayanagiri is

(a) 1139.4 km

(b) 577.52 km

(c) 1937 km

(d) 1025.36 km

Answer: (c) 1937 km

(2) If a mile stone very far away from, makes 45 to the top of Mullanyangiri mountain .So, find the distance of this mile stone form the mountain.

(a) 1118.327 km

(b) 566.976 km

(3) The distance of the satellite from the ground is

Answer: (b) 577.52 km

(4) The distance of the satellite from the top of Nanda Devi is

Answer: (a) 1139.4 km

(5) What is the angle of elevation if a man is standing at a distance of 7816m from Nanda Devi?

Answer: (b) 45°

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  • Important Questions for Class 10 Maths Chapter 9 - Some Applications of Trigonometry

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CBSE Class 10 Maths Important Questions Chapter 9 - Some Applications of Trigonometry - Free PDF Download

Trigonometry is always an important concept in mathematics. Although some may find it a complicated topic, once the basics are straightforward, it is very easy to tackle various levels. Moreover, practising is the best tool for any math concept, the same as trigonometry. Applications of trigonometry can be seen in many daily life cases. Furthermore, it is a very scoring topic for board exams too. Class 10 Maths Chapter 9 is an important topic from the exam point of view. Good capture of this topic will help you score good marks from the exam point of view.

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Important Questions for CBSE Class 10 Maths Chapter 9 - Free PDF Download

Important questions for class 10 maths chapter 9 – Applications of Trigonometry are prepared with the vision to enable students to understand the essential topics of the chapter and study accordingly. Practising these questions can bring in-depth knowledge for students on the same subject. It is known that conceptual understanding has a pivotal role in maths. Students would be able to do questions only after they understand the concept in a clear cut manner. Moreover, practising these questions can give an excellent idea to understand which portions weigh more and know from where we have to expect questions for the board exam.

Applications of Trigonometry:

Applications of trigonometry chapter is a continuation of the previous chapter of trigonometry. Here we deal with applications of the concepts learned in the chapter trigonometry. We use the concepts of trigonometry learned during the last chapter to solve questions that include situations that we may face in our daily lives.

Suppose if you are standing near a tall building and you want to measure its height, or else suppose you are just standing on a bridge across a river and you want to measure a river's width. How can you measure the height of the building and the width of the river in both cases?

To measure the building's length, we have to go to the top of the building, drop a tall rope, and then measure the string's length. Calculating the width of the river can be more difficult as if we have to stand on both sides of the river with a long rope. These methods may seem weird for most of us as they do not seem practical. But once you are now trigonometry, the task will be easy.

Applications of trigonometry can very well be used to measure heights and distances too in an accurate manner. Trigonometry has several other applications. However, to get into the trigonometry applications, it is imperative to revise the basics of trigonometry.

Basics of Trigonometry

Trigonometric ratios form the basic step of each question from the topic. Trigonometric ratios are always derived from the sides of the right angle. Let us see some of the standard ratios used for applying trigonometry:

Sin = Perpendicular / Hypotenuse

Cos = Base / Hypotenuse

Tan = Perpendicular / Base 

Cosec = 1 / sin =Hypotenuse / Perpendicular

Sec = 1 / cos = Hypotenuse / Base

Cot = 1 / tan = Base / Perpendicular

To solve any question on heights and distances, the first and foremost thing is to draw a clean, neat, and friendly diagram labelling all the available angles and sides. The point of observation or measurement should also be included as a point in the triangle representing the question. Right angle or 90 degree is necessary to apply trigonometric ratios in such problems. The height, base, and hypotenuse should also be appropriately marked in the diagram to simplify it.

Line of Sight

Line of sight is a critical concept in trigonometry as it is based on the line of sight that angle of elevation and angle of depression is measured. When we look upon an object, an imaginary straight line connects our eyes, and the object is called the line of sight.

The angle of elevation is the angle made between the horizontal and our line of vision when we look up, and angle of depression is the angle between horizontal and the line of vision when we look down upon an object.

Besides the right angle or 90-degree angle, the angle of elevation and angle of depression plays a significant role in measuring the height of buildings or the height of any such things from an observer's point of view. Based on these angles, trigonometric ratios are applied, and the base and height are decided. If we look upon a building whose height is to be measured, the angle made is the angle of elevation, and if we are looking down for something whose depth is to be measured, the angle made is the angle of depression.

The unknown values which represent the height or distance to be measured are calculated in such a way by applying equations of trigonometric ratios to both known and unknown values. From it, the unknown is calculated. We must always take care that the unknown value should represent any one of the equation variables and apply trigonometric ratio, which includes that side. The unknown value may be based on, height or hypotenuse of the triangle. 

Practising Important Questions of Class 10 Maths Chapter 9- Applications of trigonometry are the ultimate method to tackle any kind of questions from the topic. As we say Practice makes a man perfect, the same is the case for trigonometry too. Once the basics are clear, students should go on solving NCERT questions and other important questions as well.

Practice Questions of Chapter 9

Some of the questions that can help students with their preparations for upcoming board examinations are mentioned below.

Find the height of the tower from 20m from the foot of the tower with an elevation angle of 30 degrees.

Answer: 11.56 m.

When a staircase is lying against a wall, it forms a 60° angle with the horizontal. Calculate the length of the ladder if the foot of the ladder is 2.5 metres from the wall.

Answer: 5 m

The angle of elevation of the top of a tower from a location 20 metres away is 30 degrees. Determine the tower's height.

Answer : 11.56 m

A flagstaff perches atop a 5m tall structure. The angle of elevation of the top of the flagstaff is 60 degrees from a point on earth, while the angle of elevation of the top of the structure is 45 degrees from the same point. Determine the flagstaff's height.

Answer:   3.65 m

The foot of a tower is reached along a straight highway. A man standing at the top of the tower notices a car approaching the foot of the tower at a consistent pace at a 30° angle of depression. The angle of dip of the automobile is found to be 60 degrees six seconds later. Calculate the time it took the car to go to the foot of the tower from this location.

Answer: 3 sec  

Solved Question and Answers

1. If sec 2A = cosec (A – 60°), where 4A is an acute angle, find the value of A.

Ans: A = 50°

2. Mahima is given the trigonometric ratio of tan θ = 5/12. How to find the trigonometric ratio of cosec θ using trigonometry formulas.

Ans: Using trigonometry formulas, cosec θ = 13/5

3. If sin θ cos θ = 5, find the value of (sin θ + cos θ) 2 using the trigonometry formulas.

Ans:  11

4. Find the exact value of sin 75° using the trigonometric identities.

Ans: Sin 75°= (√3 + 1)/2√2

5. Given 15 cot A = 8, find sin A and sec A

Ans: sin A = 15/17 and sec A = 17/8.

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Ensures questions cover every important topic to prevent any oversight by students.

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Practising Vedantu's important questions offers profound insights into the topic.

Clarifies fundamental concepts, fostering a clear understanding.

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Simplifies applications of trigonometry, making it easier for students.

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Assures that the chapter offers the best and most essential questions, ensuring interest and ease of understanding.

Trigonometry is about understanding the relationships in right-angled triangles, especially the ratios of their sides called trigonometric ratios. The article above shares essential trigonometric formulas and introduces "Important Questions for Class 10 Maths Chapter 9 - Some Applications of Trigonometry." These questions help you apply trigonometry in real situations, making it easier to grasp. Connecting theory with practical examples, this resource becomes a handy guide, ensuring you get the hang of trigonometric concepts and their use in triangles. It's like a toolkit for tackling math problems related to triangles. 

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FAQs on Important Questions for Class 10 Maths Chapter 9 - Some Applications of Trigonometry

1. Why is Trigonometry a Difficult Topic for Many Students? Is there Any Method Through Which it Can be Learned Easily?

It is only a myth that trigonometry is a scarily difficult topic. Yes, it is true that some may find it difficult to solve the problems of the chapter, but every chapter may have such issues. But success lies where we do not stop trying more and more unless we become experts on the topic. As we the way to success do not have any shortcuts, the same is the trigonometry case. We have to first be thorough with all the trigonometric ratios and equations and then learn to draw diagrams in the most accurate manner and then keep on practising and practising. Our team's important questions at Vedantu can help you a lot in this process. We can assure you that none of your topics is left uncovered once you have done all the questions prepared by us. Practice questions to the maximum so that you become able to solve problems at lightning speed. Practising more is equal to scoring more and more. So, once the basics are clear, collect questions from whatever sources possible and start solving them at the earliest.

2. Is Trigonometry and Applications of Trigonometry Merely a Piece for Academic Scoring? Or Whether it Has Any Purpose in Our Daily Life?

Actually, there is a false belief that there is something merely for academics. Everything that we learn in our books will surely have some applications in our daily life. The truth is that we are just not aware of it. The same is the case for trigonometry and also for applications of trigonometry. From the name of the chapter – Applications of trigonometry itself, we can understand that it is an application-oriented chapter. In many cases, such as finding length, depth, distance, etc., were measured by the manual process can turn into a very hectic process, applications of trigonometry have helped us. Instead of using many instruments for measuring, with just a pen and paper and some trigonometric ratios, we can do the same. Trigonometry finds wide applications in the field of architecture, engineering, and many such. Besides in daily life, when coming to academics also, trigonometry is a very scoring chapter that can be easily dealt with if we have practised enough. As every bookish knowledge is meant to be applied in our life, the same is the case for trigonometry too. 

3. What is the significance of Chapter 9 “Some Applications of Geometry” of Class 10 Maths?

Chapter 9 “Some Applications of Geometry” of Class 10 Maths has much significance both from the examination perspective as well as due to its applications in our daily lives. 

For exams, this chapter is important because i) it can carry around 6 marks ii) it is a chapter that can help you score high in exams.

Moreover, this concept has several applications in fields like Engineering, Criminology, Marine Biology, Constructions, Aeronautics, Navigation, Physics, measuring the heights of buildings, mountains, etc. Hence, learning it will be beneficial. 

4. How can I download Vedantu’s Important Questions for Chapter 9 “Some Applications of Geometry” of Class 10 Maths.

To download these questions:

Click on Vedantu’s Important Questions for Chapter 9 “Some Applications of Geometry."

Click on the option to "Download PDF" when you scroll down on the following page.

This will redirect you to the next page containing the link to download the required PDF promptly.

Otherwise, you can install the Vedantu Mobile app. You can then download these important questions from the mobile app. Nonetheless, both these methods do not incur any cost. 

5. What are the significant features of Vedantu’s Important Questions for Chapter 9 “Some Applications of Geometry” of Class 10 Maths?

These are the very advantageous features of Vedantu's Important Questions:

These are cautiously selected by expert teachers.

These have been put together after screening several sample papers, mock papers, reference books, and previous years' question papers.

These have been systematically arranged as per the marking scheme of 1 to 5 marks questions.

 The solutions to these questions are prepared especially to focus on the CBSE board examinations.

These are available to be downloaded free of charge.

6. What should I do if I find Chapter 9 “Some Applications of Geometry” of Class 10 Maths difficult?

It is perfectly normal for students to find certain chapters intimidating. However, the first step to get over this is to let go of the fear. Analyze why you find the chapter complicated and work on the problem areas in parts.

Read the text thoroughly and refer to visual aids to help in enhanced understanding. Ask your teachers in case of doubts. You can also opt for Vedantu's one-on-one classes for the same. Practising a good number of problems will help you overcome any fear.

7. What are the three main topics taught in Chapter 9 “Some Applications of Geometry” of Class 10 Maths?

The three major topics that help in understanding various applications of trigonometry are as follows:

Line of sight: refers to a straight line from the eye of the observer to the object

Angle of elevation: the angle formed by the line of sight and the horizontal line. This happens in case the observer is looking upwards at the object.

Angle of depression: the angle formed by the line of sight and the horizontal line. This is used when the observer is looking downwards at the object.

CBSE Class 10 Maths Important Questions

Cbse study materials.

  • Class 10 Maths

Important Questions Class 10 Maths Chapter 9 Applications of Trigonometry

Important questions for Class 10 Maths Chapter 9 Some Applications of Trigonometry are provided here for the board exams preparation. The questions are based on the new pattern of CBSE and are as per the revised syllabus. Students who are preparing CBSE 2022-2023 Maths exam are advised to practice these important questions of Some Applications of Trigonometry For Class 10 . Solving these questions will help students to score high marks in the questions asked from this chapter.

Trigonometry has more applications in our daily existence, and hence, the chapter is crucial for the board exam and valuable in many other fields. Most of the questions from this chapter are also asked in the competitive exams such as JEE etc.

  • Applications of Trigonometry
  • Trigonometry Formula For Class 10
  • Trigonometry Table

Below, we have provided the questions of Chapter 9 Applications of Trigonometry with the solutions. Students can als o find additional qu estions without solutions for their practice.

Important Questions & Answers For Class 10 Maths Chapter 9 – Some Applications of Trigonometry

Q.1: The shadow of a tower standing on level ground is found to be 40 m longer when the Sun’s altitude is 30° than when it is 60°. Find the height of the tower.

Let AB be the tower and BC be the length of its shadow when the sun’s altitude (angle of elevation from the top of the tower to the tip of the shadow) is 60° and DB be the length of the shadow when the angle of elevation is 30°.

Important questions class 10 maths chapter 9 A1

Let us assume, AB = h m, BC = x m

DB = (40 +x) m

In the right triangle ABC,

tan 60° = AB/BC

h = √3 x……….(i)

In the right triangle ABD,

tan 30° = AB/BD

1/√3 =h/(x + 40) ……..(ii)

From (i) and (ii),

x(√3 )(√3 ) = x + 40

3x = x + 40

Substituting x = 20 in (i),

Hence, the height of the tower is 20√3 m.

Q. 2: A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

Using given instructions, draw a figure. Let AC be the broken part of the tree. Angel C = 30 degrees.

To Find: Height of the tree, which is AB

Important questions class 10 maths chapter 9 A2

From figure: Total height of the tree is the sum of AB and AC i.e. AB+AC

In right ΔABC,

Using Cosine and tangent angles,

cos 30° = BC/AC

We know that, cos 30° = √3/2

√3/2 = 8/AC

AC = 16/√3 …(1)

tan 30° = AB/BC

1/√3 = AB/8

AB = 8/√3 ….(2)

From (1) and (2),

Total height of the tree = AB + AC = 16/√3 + 8/√3 = 24/√3 = 8√3 m.

Q. 3: Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

Let AB and CD be the poles of equal height.

O is the point between them from where the height of elevation is taken. BD is the distance between the poles.

Important questions class 10 maths chapter 9 A3

As per the above figure, AB = CD,

OB + OD = 80 m

In right ΔCDO,

tan 30° = CD/OD

1/√3 = CD/OD

CD = OD/√3 … (1)

In right ΔABO,

tan 60° = AB/OB

√3 = AB/(80-OD)

AB = √3(80-OD)

AB = CD (Given)

√3(80-OD) = OD/√3 (Using equation (1))

3(80-OD) = OD

240 – 3 OD = OD

Substituting the value of OD in equation (1)

CD = 20√3 m

⇒ OB = (80-60) m = 20 m

Therefore, the height of the poles are 20√3 m and the distance from the point of elevation are 20 m and 60 m respectively.

Q. 4:  An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Let AB be the height of the observer and PR be the height of the tower.

Also, PB is the distance between the foot of the tower and the observer.

Consider θ as the angle of elevation of the top of the tower from the eye of the observer.

Important questions class 10 maths chapter 9 A4

From the above figure,

AB = PQ = 1.5 m

PB = QA = 20 m

QR = PR – PQ = 22 – 1.5 = 20.5 m

In the right triangle AQR,

tan θ = QR/AQ

tan θ = 20.5/20.5 = 1

⇒ tan θ = tan 45°

Hence, the angle of elevation is 45°.

Q. 5: The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is √st.

Let BC = s; PC = t

Let the height of the tower be AB = h.

∠ABC = θ and ∠APC = 90° – θ

(∵ the angle of elevation of the top of the tower from two points P and B are complementary)

Important questions class 10 maths chapter 9 A5

In triangle ABC,

tan θ = AC/BC = h/s ………..(i)

In triangle APC,

tan (90° – θ) = AC/PC = h/t

cot θ = h/t ………..(ii)

Multiplying (i) and (ii),

tan θ × cot θ = (h/s) × (h/t)

1 = h 2 /st

Hence, the height of the tower is √st.

Q.6: The angle of elevation of the top of a tower from a certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower.

Let AB be the height of the tower.

The angle of elevation of the top of a tower from point P is 30°, i.e. ∠APB = 30°.

Given that, when the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°.

Thus, PQ = 20 m

Important questions class 10 maths chapter 9 A6

Also, ∠AQB = 30° + 15° = 45°.

In right triangle ABQ,

tan 45° = AB/QB

h = x….(i)

In right triangle ABP,

tan 30° = AB/PB

1/√3 = h/(x + 20)

x + 20 = √3h  {from (i)}

h + 20 = √3h

√3h – h = 20

h = 20/(√3 – 1)

h = [20/(√3 – 1)] × [(√3 + 1)/(√3 + 1)]

= 20(√3 + 1)/(3 – 1)

= 20(√3 + 1)/2

= 10(√3 + 1)

Therefore, the height of the tower is 10(√3 + 1) m.

Q.7: A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.

Let AB be the vertical pole and AC be the length of the rope.

Also, the angle of elevation = ∠ACB = 30°

Important questions class 10 maths chapter 9 A7

In right triangle ABC,

sin 30 = AB/AC

1/2 = AB/20

AB = 20/2 = 10

Therefore, the height of the vertical pole is 10 m.

Q.8: From the top of a 7 m high building, the angle of elevation of the top of a cable tower is

60° and the angle of depression of its foot is 45°. Determine the height of the tower.

Let AB be the height of the building and CE be the height of the tower.

Also, A be the point from where the elevation of the tower is 60° and the angle of depression of its foot is 45°.

EC = DE + CD

Important questions class 10 maths chapter 9 A8

From the figure,

CD = AB = 7 m

tan 45° = AB/BC

BC = 7 {since BC = AD}

Thus, AD = 7 m

In right triangle ADE,

tan 60° = DE/AD

⇒ DE = 7√3 m

EC = DE + CD = (7√3 + 7) = 7(√3 + 1)

Therefore, the height of the tower is 7(√3 + 1) m.

Video Lesson on Applications of Trigonometry

applications of trigonometry case study questions

Practice Questions For Class 10 Maths Chapter 9 Some Applications of Trigonometry

  • The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, what is the height of the hill? [Answer: 150 m]
  • A bridge across the river makes an angle of 45° with the river bank. If the length of the bridge across the river is 150 m, what is the width of the river? [Answer: 75√2 m]
  • There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are the points directly opposite to each other on the two banks, and in a line with the tree. If the angles of elevation of the top of the tree from P and Q are 30° and 45° respectively, find the height of the tree. [Answer: 36.6.m]
  • From a point 20m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower. [Answer: 11.56 m]
  • A flagstaff stands at the top of a 5m high tower. From a point on the ground, the angle of elevation of the top of the flagstaff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flagstaff. [Answer: 3.65 m]
  • A tower subtends an angle α at a point A in the place of its base and the angle of depression of the foot of the tower at a point b ft. just above A is β. Prove that the height of the tower is b tan α cot β.
  • A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. From a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 45°. Find the height of the tower. [Answer: 9.55m]
  • The angle of elevation of a cloud from a point h metres above the surface of a lake is θ and the angle of depression of its reflection in the lake is φ. Prove that the height of the cloud above the lake is h[(tan φ + tan θ)/ (tan φ – tan θ)].
  • The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings. [Answer: 4(3 + √3) m]
  • A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower at a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point. [Answer: 3 sec]

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Class 10 Maths Case Study Questions Chapter 8 Introduction to Trigonometry

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Case study Questions in the Class 10 Mathematics Chapter 8  are very important to solve for your exam. Class 10 Maths Chapter 8 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 8  Introduction to Trigonometry

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In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Introduction to Trigonometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 8 Introduction to Trigonometry

Case Study/Passage-Based Questions

Question 1:

applications of trigonometry case study questions

Answer: (d) 6m

(ii) Measure of ∠A =

Answer: (c) 45°

(iii) Measure of ∠C =

(iv) Find the value of sinA + cosC.

Answer: (d) 2√2

(v) Find the value of tan 2 C + tan 2  A.

Answer: (c) 2

Question 2:

applications of trigonometry case study questions

Answer: (a) 30°

(ii) The measure of  ∠C is

Answer: (c) 60°

(iii) The length of AC is 

Answer: (d)6√3m

(iv) cos2A =

Answer: (b)1/2

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Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

Q. Write the value of sec 30°.

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

A straight highway leads to the foot of tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°.

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

horizontal line

Vertical line

Line of sight

Parallel lines

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

Let the speed of car be v m/s.

Let car takes t seconds to reach the point B from the point D

Distance travel by car in t sec = vt m.

In ΔABD, we have

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

h = √3 vt ...(i)

and in right D ABC, we have

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

Q. Write the value of cosec 60°.

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

Q. If the two lines are parallel; then the alternate opposite angles are ..................... .

None of these

Form a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and angle of elevation of the top of the flagstaff from P is 45°.

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

Q. What is the value of tan 45°?

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

AP = 10 √3 m

In right ΔPAD,

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

10 √3 = 10 + BD

BD = 10 √3 – 10

BD = 7.32 m.

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

BP 2 = AB 2 + AP 2

AB 2 = AP 2 + BP 2

AP 2 = AB 2 + BP 2

None of these.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

Acute angled triangle

Right angled triangle

Obtuse angled triangle

Equilateral triangle.

From a point on the bridge across a river the angle of depression of the banks on opposite sides of the river 30° and 45° respectively.

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

Q. The value of tan 45° is

The value of tan 45° is = 1

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

1(√3 + 1) m

3(√3 + 1) m

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

In ΔPDB, ∠B = 45°

tan 45° = PD/DB

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

width of the river = AB = AD + DB

= 3(√3 + 1)m.

Class 10 Maths Chapter 9 Case Based Questions - Some Applications of Trigonometry

Perpendicular/Base

Base/Perpendicular

Hypotenuse/Base

Perpendicular/Hypotenuse

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CBSE Case Study Questions for Class 10 Maths Trigonometry Free PDF

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Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Trigonometry  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 10 Maths Trigonometry PDF

Checkout our case study questions for other chapters.

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  • Chapter 7 Coordinate Geometry Case Study Questions
  • Chapter 9 Some Applications of Trigonometry Case Study Questions
  • Chapter 10 Circles Case Study Questions

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applications of trigonometry case study questions

Class 10th Maths - Some Applications of Trigonometry Case Study Questions and Answers 2022 - 2023

By QB365 on 09 Sep, 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 10th Maths Subject - Some Applications of Trigonometry, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

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Some applications of trigonometry case study questions with answer key.

10th Standard CBSE

Final Semester - June 2015

Case Study 

applications of trigonometry case study questions

(ii) Measure of \(\angle\) ACB is equal to

(iii) Width of the river is 

(iv) Height of the other temple is

(v) Angle of depression is always

applications of trigonometry case study questions

(ii) Value of DF is equal to

(iii) Value of h is

(iv) Height of the balloon from the ground is

(v) If the balloon is moving towards the building, then both angle of elevation will

applications of trigonometry case study questions

(ii) If the angle made by the rope to the ground level is 45°, then find the distance between artist and pole at ground level.

(iii) Find the height of the pole if the angle made by the rope to the ground level is 30°.

(iv) If the angle made by the rope to the ground level is 30° and 3 m rope is broken, then find the height of the pole

(v) Which mathematical concept is used here?

applications of trigonometry case study questions

(ii) If fireman place the ladder 5 m away from the wall and angle of elevation is observed to be 30°, then length of the ladder is

(iii) If fireman places the ladder 2.5 m away from the wall and angle of elevation is observed to be 60°, then find the height of the window. (Take \(\sqrt{3}\) = 1.73)

(iv) If the height of the window is 8 m above the ground and angle of elevation is observed to be 45°, then horizontal distance between the foot of ladder and wall is

(v) If the fireman gets a 9 m long ladder and window is at 6 m height, then how far should the ladder be placed?

applications of trigonometry case study questions

(ii) What should be the length of ladder, so that it makes an angle of 60° with the ground?

(iii) The distance between the foot ofladder and pole is

(iv) What will be the measure of \(\angle\) BCD when BD and CD are equal?

(v) Find the measure of \(\angle\) DBC.

applications of trigonometry case study questions

(ii) Distance between two positions of the car is

(iii) Total time taken by the car to reach the foot of the building from starting point is

(iv) The distance of the observer from the car when it makes an angle of 60° is

(v) The angle of elevation increases

applications of trigonometry case study questions

(ii) If  \(\angle\) YAB = 30°, then \(\angle\) ABD is also 30°, Why?

(iii) Length of CD is equal to

(iv) Length of BD is equal to

(v) Length of AC is equal to

applications of trigonometry case study questions

(ii) If the height of the pedestal is 20 m, then the height of the statue is

(iii) If the height of the statue is 1.6 m, then height of the pedestal is

(iv) If the total height of the statue and pedestal is 39 m, then find the length of AC.

(v) If the height of the pedestal is 35 m, then length of AD is

applications of trigonometry case study questions

(ii) If the position of Pankaj is 25 m away from the base of pedestal and Zr = 30°, then find the height of pedestal.

(iii) If the height of pedestal is 30 m, \(\angle\) t = 45° and \(\angle\) z = 30°, then the horizontal distance between Arun and Pankaj is

(iv) If the vertical height of sky lantern from the top of pedestal is 12 m and \(\angle\) y = 30°, then distance between Teewan and sky lantern is

(v) If \(\angle\) q = 60° and position of Arun is 15 m away from the base of pedestal, then find the height of pedestal.

applications of trigonometry case study questions

(ii) Find the length of RO.

(iii) The width of the road is

(iv) If the angle of elevation made by pole PQ is 45°, then the length of PO =

(v) Angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level is known as

applications of trigonometry case study questions

(ii) If the top of broken part of a tree touches the ground at a point whose distance from foot of the tree is equal to height of remaining part, then its angle of inclination is

(iii) The angle of elevation are always

applications of trigonometry case study questions

(v) If the height of a tree is 6 m, which is broken by wind in such a way that its top touches the ground and makes an angles 30° with the ground. At what height from the bottom of the tree is broken by the wind?

applications of trigonometry case study questions

(iii) Width of the river is

(iv) The angles of elevation and depression are always

(v) If BD = 21 m, then height of the bridge is

applications of trigonometry case study questions

(ii) The value of PD is

applications of trigonometry case study questions

(v) If A and B are two objects and the eye of an observer is at point 0, then the line of sight will be

applications of trigonometry case study questions

(ii) If the distance between the position of pigeon increases, then the angle of elevation

(iii) Find the distance between the boy and the pole.

(iv) How much distance the pigeon covers in 8 seconds?

(v) Find the speed of the pigeon

applications of trigonometry case study questions

(ii) Find the length of GH.

(iii) The length of second step is 

(iv) The length of PQ =

(v) The length of first step is

*****************************************

Some applications of trigonometry case study questions with answer key answer keys.

applications of trigonometry case study questions

(i) (b): The person who makes small angle of elevation is more closer to the balloon. \(\therefore\) Radlra is more closer to the balloon. (ii) (b):  \(\text { In } \Delta E F D, \tan 30^{\circ}=\frac{E D}{D F}\) \(\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{h}{D F} \) \(\Rightarrow \quad D F=h \sqrt{3} \mathrm{~m}\) (iii) (a): In \(\Delta\) GCE, \(\begin{array}{l} \tan 60^{\circ}=\frac{E C}{G C}=\frac{h+4}{D F} \\ \Rightarrow \quad \sqrt{3}=\frac{h+4}{\sqrt{3} h} \Rightarrow 3 h=h+4 \Rightarrow h=2 \end{array}\) (iv) (c): Height of the balloon from the ground = BE = BC + CD + DE = 2 + 4 + 2 = 8 m (v) (b)

applications of trigonometry case study questions

(i) (b): Total height of pole = 8 m \(\therefore\) BD = AD - AB = (8 - 2)m = 6 m (ii) (a):  \(\text { In } \Delta B D C, \frac{B D}{B C}=\sin 60^{\circ}\) \(\Rightarrow \quad \frac{6}{B C}=\frac{\sqrt{3}}{2} \) \(\Rightarrow \quad B C=\frac{12}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=4 \sqrt{3} \mathrm{~m}\) (iii) (d):  \(\text { In } \triangle B D C\) \(\frac{B D}{C D}=\tan 60^{\circ} \Rightarrow \frac{6}{C D}=\sqrt{3} \Rightarrow C D=\frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=2 \sqrt{3} \mathrm{~m}\) (iv) (b) :  \(\text { If } \Delta B C D\) \(\frac{B D}{C D}=\tan \theta \Rightarrow 1=\tan \theta \quad[\because B D=C D] \) \(\Rightarrow \quad \theta=45^{\circ}\) (v) (c) :   \(\operatorname{In} \Delta B D C, \angle B+\angle D+\angle C=180^{\circ}\) \(\therefore \quad \angle B=180^{\circ}-60^{\circ}-90^{\circ}=30^{\circ}\)

(i) (c):   \(\text { In } \Delta A B C, \frac{A B}{B C}=\tan 60^{\circ}\) \(\Rightarrow \quad A B=25 \times \sqrt{3}\) \(\therefore\) Height of building is 25 \(\sqrt{3}\) m . (ii) (b):   \(\text { In } \Delta A B D, \frac{A B}{B D}=\tan 30^{\circ}\) \(\Rightarrow \frac{25 \sqrt{3}}{B D}=\frac{1}{\sqrt{3}} \Rightarrow B D=75 \mathrm{~m}\) \(\therefore\)  Distance between two positions of car = (75 - 25) m = 50m. (iii) (d): Time taken to cover 50 m distance = 6 sec. \(\therefore\) Time taken to cover 25 m distance = 3 sec. \(\therefore\) Total time taken by car = 6 sec + 3 sec = 9 sec (iv) (c):  \(\text { In } \Delta A B C, \frac{B C}{A C}=\cos 60^{\circ}\) \(\Rightarrow \quad \frac{25}{A C}=\frac{1}{2} \) \(\Rightarrow A C=50 \mathrm{~m}\) (v) (a)

(i) (b):   \(\angle X A C=45^{\circ}\)   \(\therefore \quad \angle A C D=45^{\circ}\)   [Alternate interior angles] (ii) (b) (iii) (c) :  \(\text { In } \Delta A C D\) \(\frac{A D}{D C}=\tan 45^{\circ} \) \(\Rightarrow \frac{100}{D C}=1 \Rightarrow D C=100 \mathrm{~m}\) (iv) (d):   \(\text { In } \Delta A B D, \frac{A D}{B D}=\tan 30^{\circ}\) \(\Rightarrow \quad \frac{100}{B D}=\frac{1}{\sqrt{3}} \) \(\Rightarrow \quad B D=100 \sqrt{3} \mathrm{~m}\) (v) (a):  \(\text { In } \Delta A D C\) \(\frac{A D}{A C}=\sin 45^{\circ} \Rightarrow \frac{100}{A C}=\frac{1}{\sqrt{2}} \Rightarrow A C=100 \sqrt{2} \mathrm{~m}\)

applications of trigonometry case study questions

(i) (c):   \(\text { In } \Delta O P Q\) ,  we have \(\tan 60^{\circ}=\frac{P Q}{P O} \) \(\Rightarrow \sqrt{3}=\frac{20}{P O} \) \(\Rightarrow P O=\frac{20}{\sqrt{3}} \mathrm{~m}\) (ii) (b): In \(\Delta\) ORS, we have \(\tan 30^{\circ}=\frac{R S}{O R} \Rightarrow \frac{1}{\sqrt{3}}=\frac{20}{O R} \Rightarrow O R=20 \sqrt{3} \mathrm{~m}\) (iii) (d): Clearly, width of the road = PR \(\begin{array}{l} =P O+O R=\left(\frac{20}{\sqrt{3}}+20 \sqrt{3}\right) \mathrm{m} \\ =20\left(\frac{4}{\sqrt{3}}\right) \mathrm{m}=\frac{80}{\sqrt{3}} \mathrm{~m}=46.24 \mathrm{~m} \end{array}\) (iv) (a):   \(\text { In } \Delta O P Q \text { , if } \angle P O Q=45^{\circ} \text { , then }\) \(\tan 45^{\circ}=\frac{P Q}{P O} \Rightarrow 1=\frac{20}{P O} \Rightarrow P O=20 \mathrm{~m}\) (v) (b)

applications of trigonometry case study questions

(i) (d) : Clearly, \(\angle\) DAC = 60° So,in \(\Delta\) ADC, we have \(\tan 60^{\circ}=\frac{C D}{A D} \Rightarrow \sqrt{3}=\frac{6}{A D} \) \(\Rightarrow A D=\frac{6}{\sqrt{3}} \mathrm{~m}\) (ii) (b): Clearly, \(\angle\) DBC = 30° So, in  \(\Delta\) BDC,we have \(\tan 30^{\circ}=\frac{C D}{B D} \) \(\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{6}{B D} \) \(\Rightarrow B D=6 \sqrt{3} \mathrm{~m}\) (iii) (b): Width of the river = AB = AD + BD \(\begin{array}{l} =\frac{6}{\sqrt{3}}+6 \sqrt{3} \\ =6\left(\frac{1}{\sqrt{3}}+\sqrt{3}\right)=6\left(\frac{4}{\sqrt{3}}\right)=\frac{24}{\sqrt{3}} \mathrm{~m}=13.87 \mathrm{~m} \end{array}\) (iv) (a): The angle of elevation and angle of depression are always acute angles. (v) (c): In \(\Delta\) BCD,if BD = 21m, then \( \tan 30^{\circ}=\frac{C D}{B D} \) \(\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{C D}{21} \Rightarrow C D=\frac{21 \sqrt{3}}{3}=7 \sqrt{3} \mathrm{~m}\)

(i) (b): In the right   \(\Delta\) ADQ, we have \(\sin 30^{\circ}=\frac{D Q}{A D} \Rightarrow \frac{1}{2}=\frac{D Q}{24}\) \(\Rightarrow \quad D Q=12 \mathrm{~m}\) Thus, distance of paraglider from the ground is 12 m. (ii) (a): We have PQ = BC = 6 m Now, as DQ = 12 m \(\therefore\) DP = DQ - PQ = 12 - 6 = 6 m (iii) (c) : In right  \(\Delta\) BDP,we have \(\sin 45^{\circ}=\frac{D P}{B D} \Rightarrow \frac{1}{\sqrt{2}}=\frac{6}{B D}\) \(\Rightarrow \quad B D=6 \sqrt{2} \mathrm{~m}\) Thus, the distance of paraglider from the girl is 6 \(\sqrt{2}\)  m. (iv) (d): \(\angle\) AOP given in figure, is the angle of depression. (v) (c): If A and B are two objects and the eye of an observer is at point 0, then line of sight will be both OA and OB.

applications of trigonometry case study questions

Given, side of square top = 2 m \(\therefore\) AB = HT = QR = CD = 2 m Also, A C and BD are perpendicular to the ground. So, AH = HQ = QC.  (By B.P.T. Theorem) (i) (b): \(\text { In } \triangle A E C\) \(\sin 60^{\circ}=\frac{A C}{A E} \Rightarrow \frac{\sqrt{3}}{2}=\frac{6}{A E} \Rightarrow A E=6.93 \mathrm{~m}\) \(\therefore\) Length of each leg i.e., AE = BF = 6.93 m. (ii) (c):   \(\text { In } \Delta A G H, \tan 60^{\circ}=\frac{A H}{G H} \Rightarrow \sqrt{3}=\frac{2}{G H}\) \(\Rightarrow G H=1.15 \mathrm{~m}\) (iii) (a) : Length of second step = GH + HT + TU = 1.15 + 2 + 1.15 = 4.3 m (iv) (b): \(\text { In } \Delta A P Q\) \(\tan 60^{\circ}=\frac{A Q}{P Q} \Rightarrow \sqrt{3}=\frac{4}{P Q} \Rightarrow P Q=\frac{4}{\sqrt{3}} \mathrm{~m}=2.31 \mathrm{~m}\) (v) (c) : Length of first step = PQ + QR + RS =2.31 + 2 + 2.31 = 6.62 m

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  1. Case Study Questions for Class 10 Maths Chapter 9 Some Applications of

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