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CBSE Important Questions for Class 10 Maths Some Applications of Trigonometry - 2025-26

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Some Applications of Trigonometry Class 10 important questions with answers 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.


Vedantu is a platform that provides free CBSE Solutions and other study materials for students. Students can register and get access to the best and reliable source of study materials specially made by master teachers at Vedantu. You can Download Maths NCERT Solutions Class 10 to help you to revise the complete Syllabus and score more marks in your examinations. Subjects like Science, Maths, Engish will become easy to study if you have access to Class 10 Science NCERT Solutions, Maths solutions, and solutions of other subjects that are available on Vedantu only.

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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.


Angles

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.

 

Question 1

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.

 

Question 2

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

 

Question 3

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

 

Question 4

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

 

Question 5

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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Conclusion

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 CBSE Important Questions for Class 10 Maths Some Applications of Trigonometry - 2025-26

1. What types of important questions can be expected from "Some Applications of Trigonometry" in Class 10 CBSE board exams?

  • 1-mark questions: Definitions (e.g., angle of elevation, line of sight)
  • 3-mark questions: Direct application problems (e.g., finding the height of a tower)
  • 5-mark questions: Multi-step or HOTS problems (e.g., combined use of elevation and depression, real-life scenarios with diagrams)

As per CBSE 2025–26, questions often combine conceptual application and diagram interpretation.

2. How do you solve a height and distance problem using trigonometric ratios in Class 10 important questions?

  • Draw a labeled right-angled triangle representing the scenario.
  • Identify the known values: angle(s), base/distance, height.
  • Select the appropriate trigonometric ratio (sine, cosine, or tangent).
  • Set up the equation and substitute values.
  • Solve for the unknown (height/distance).

3. Why is the line of sight critical in Class 10 Trigonometry important questions?

The line of sight defines the direct imaginary path between the observer and the object, allowing calculation of the angle of elevation or depression, which is essential for accurately applying trigonometric ratios to solve heights and distances questions.

4. What common mistakes should students avoid in "Some Applications of Trigonometry" important questions?

  • Confusing angle of elevation with angle of depression.
  • Not aligning the diagram with the problem statement.
  • Using the wrong trigonometric ratio.
  • Incorrect unit conversion (e.g., meters to centimeters).
  • Ignoring the sum of heights if objects stand one atop another.

5. How can students quickly identify which trigonometric ratio to use in an important question?

Analyze which sides of the triangle are given and needed (perpendicular, base, hypotenuse):

  • If you have opposite and adjacent, use tan (tan θ = perpendicular/base).
  • If you need opposite and hypotenuse, use sin (sin θ = perpendicular/hypotenuse).
  • If you want adjacent and hypotenuse, use cos (cos θ = base/hypotenuse).

6. What is the exam trend or marking weightage for Class 10 Trigonometry application questions in CBSE?

As per CBSE 2025–26, application-based questions from "Some Applications of Trigonometry" generally carry 3 to 5 marks each, totaling around 6 marks per paper. These can span direct, HOTS, and case-study items.

7. How can the concepts of angle of elevation and depression be differentiated in CBSE important questions?

  • Angle of elevation: Observer looks up from horizontal to an object above.
  • Angle of depression: Observer looks down from horizontal to an object below.

Students should sketch and mark these accurately in diagrams during board answers.

8. Why are diagram-based questions frequently included in "Some Applications of Trigonometry" Class 10 important questions?

Diagram-based questions assess a student’s ability to translate real-life or word problems into geometric representations, which is key for accurate application of trigonometric ratios. CBSE prioritizes these for conceptual clarity as per the 2025–26 syllabus.

9. What is a high-order thinking skill (HOTS) question in the context of Class 10 Trigonometry applications?

A HOTS question requires students to apply trigonometric ratios in multi-step or unfamiliar scenarios, often combining angles of elevation and depression, or requiring reasoning to select appropriate triangles and relationships in complex problems.

10. How can previous year important questions benefit Class 10 students studying this chapter?

  • Familiarize students with question patterns and marking schemes.
  • Reveal common examiner preferences and variations.
  • Boost confidence through practice of real exam-level application problems.

11. In exam questions, how should students handle cases where two observers view the same object from different angles?

Draw two right-angled triangles sharing a common vertical or horizontal side, assign appropriate angles and distances, and set up equations using two trigonometric ratios. Solve the system of equations to find the required height or distance.

12. What pitfalls lead to loss of marks in "Some Applications of Trigonometry" important questions?

  • Not showing labeled diagrams.
  • Missing stepwise calculation.
  • Not specifying units in answers.
  • Inaccurate rounding of decimal values.

13. What is the role of trigonometry applications outside the classroom, as per CBSE important question themes?

Applications include measuring inaccessible heights (mountains, towers), distances across rivers, and are foundational in fields like navigation, engineering, architecture, and astronomy, making them relevant both academically and in daily life scenarios.

14. How can a student effectively prepare for important questions from "Some Applications of Trigonometry" for the CBSE board?

  • Practice with a variety of problems (direct and HOTS).
  • Regularly draw and label diagrams.
  • Review common trigonometric ratios and CBSE formulas.
  • Attempt previous years’ important questions and sample papers.

15. What approach should be used if a question involves both the sum and difference of heights in a trigonometry application scenario?

Carefully assign variables to each individual height, use two separate equations for the scenarios (e.g., person standing on a building, flag on pole), and solve the system for the required quantity, ensuring all logical steps are shown as per CBSE standards.