CBSE Class 10 Mathematics (Standard) Chapter 9 Some Applications of Trigonometry Important Questions 2027
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22 questions from Some Applications of Trigonometry appeared in 7 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Trigonometry unit — 12 marks in the official syllabus
- Asked in 7 of 7 analysed papers (2022–2026)
- About 3.1 questions per paper (OR alternatives counted separately)
- 4 question patterns repeated across papers
Important topics in Some Applications of Trigonometry
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Heights and distances - two angles / two positions | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 2 | Heights and distances - single elevation/depression | Board 2025Board 2026Sample 2026 | ★★☆☆☆ |
| 3 | Heights and distances - two objects (tower + building etc.) | Board 2022Board 2023 | ★☆☆☆☆ |
Repeated questions from Some Applications of Trigonometry
1. Two positions with changing angle (30/45/60)
3×Board 2026Sample 2025Sample 20261/2/5 marks
[case context: Tejas on top of a building observes a car approaching at uniform speed; angle of depression changes from 30 degrees to 60 degrees in 6 seconds, and at 60 degrees the car is 25 m from the building] What is the distance between the two positions of the car ?
2. One-ratio slant distance conversion
3×Board 2025Board 20261/2 marks
[case context: Amrita sees top of a lighthouse at elevation 60 deg from ground; from an observation deck 40 m higher the elevation is 45 deg; figure with A ground point, B deck, C top, h = CD] Find distance BC in terms of 'h'.
3. One-step tan: find height or distance
2×Board 2026Sample 20261 marks
From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be 45 degrees. The height (in metres) of the tower is : (A) 10 sqrt(3) (B) 30 sqrt(3) (C) 60 (D) 30
4. Mutual elevations between two structures
2×Board 2022Board 20233/5 marks
The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is 60 degrees. The angle of elevation of the top of second tower from the foot of the first tower is 30 degrees. Find the distance between two towers and the height of the other tower. Also, find the length of the wire attached to the tops of both the towers.
Some Applications of Trigonometry questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 4 | 10 |
| Board 2023 | 2 | 10 |
| Board 2024 | 1 | 5 |
| Board 2025 | 5 | 7 |
| Sample 2025 | 1 | 5 |
| Board 2026 | 5 | 7 |
| Sample 2026 | 4 | 6 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Some Applications of Trigonometry
Board 2026 5 questions
From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be 45 degrees. The height (in metres) of the tower is : (A) 10 sqrt(3) (B) 30 sqrt(3) (C) 60 (D) 30
[case context: Tejas on top of a building observes a car approaching at uniform speed; angle of depression changes from 30 degrees to 60 degrees in 6 seconds, and at 60 degrees the car is 25 m from the building] What is the height of the building ?
[case context: Tejas on top of a building observes a car approaching at uniform speed; angle of depression changes from 30 degrees to 60 degrees in 6 seconds, and at 60 degrees the car is 25 m from the building] What is the distance between the two positions of the car ?
[case context: Tejas on top of a building observes a car approaching at uniform speed; angle of depression changes from 30 degrees to 60 degrees in 6 seconds, and at 60 degrees the car is 25 m from the building] What would be the total time taken by the car to reach the foot of the building from the starting point ?
[case context: Tejas on top of a building observes a car approaching at uniform speed; angle of depression changes from 30 degrees to 60 degrees in 6 seconds, and at 60 degrees the car is 25 m from the building] What is the distance of the observer from the car when it makes an angle of 60 degrees ?
Sample 2026 4 questions
[case context: India Gate, 42m tall monument at New Delhi; student Shreya of height 1m visits it] What is the angle of elevation from Shreya's eye to the top of India Gate, if she is standing at a distance of 41m away from the India Gate?
[case context: India Gate, 42m tall; observer Shreya of height 1m] If Shreya observes the angle of elevation from her eye to the top of India Gate to be 60 degrees, then how far is she standing from the base of the India Gate?
[case context: India Gate, 42m tall; observer Shreya of height 1m] If the angle of elevation from Shreya's eye changes from 45 degrees to 30 degrees, when she moves some distance back from the original position, find the distance she moves back.
[case context: India Gate, 42m tall; observer Shreya of height 1m] If Shreya moves to a point which is at a distance of 41/sqrt(3) m from the India Gate, then find the angle of elevation made by her eye to the top of India Gate.
Board 2025 5 questions
A kite is flying at a height of 150 m from the ground. It is attached to a string inclined at an angle of 30 deg to the horizontal. The length of the string is : (A) 100*sqrt(3) m (B) 300 m (C) 150*sqrt(2) m (D) 150*sqrt(3) m
[case context: Amrita sees top of a lighthouse at elevation 60 deg from ground; from an observation deck 40 m higher the elevation is 45 deg; figure with A ground point, B deck, C top, h = CD] If CD is h metres, find the distance BD in terms of 'h'.
[case context: Amrita sees top of a lighthouse at elevation 60 deg from ground; from an observation deck 40 m higher the elevation is 45 deg; figure with A ground point, B deck, C top, h = CD] Find distance BC in terms of 'h'.
[case context: Amrita sees top of a lighthouse at elevation 60 deg from ground; from an observation deck 40 m higher the elevation is 45 deg] Find the height CE of the lighthouse [Use sqrt(3) = 1.73]
[case context: Amrita sees top of a lighthouse at elevation 60 deg from ground; from an observation deck 40 m higher the elevation is 45 deg] Find distance AE, if AC = 100 m.
Sample 2025 1 question
A boy whose eye level is 1.35 m from the ground, spots a balloon moving with the wind in a horizontal line at some height from the ground. The angle of elevation of the balloon from the eyes of the boy at an instant is 60 deg. After 12 seconds, the angle of elevation reduces to 30 deg. If the speed of the wind is 3 m/s then find the height of the balloon from the ground. (Use sqrt(3) = 1.73)
Board 2024 1 question
A pole 6 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point P on the ground is 60 degrees and the angle of depression of the point P from the top of the tower is 45 degrees. Find the height of the tower and the distance of point P from the foot of the tower. (Use sqrt(3) = 1.73)
Board 2023 2 questions
The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is 60 degrees. The angle of elevation of the top of second tower from the foot of the first tower is 30 degrees. Find the distance between two towers and the height of the other tower. Also, find the length of the wire attached to the tops of both the towers.
A spherical balloon of radius r subtends an angle of 60 degrees at the eye of an observer. If the angle of elevation of its centre is 45 degrees from the same point, then prove that height of the centre of the balloon is sqrt(2) times its radius.
Board 2022 4 questions
[case context: Gadisar Lake chhatri; from point A at h m above water level, angle of elevation of top of Chhatri (point B) is 45 degrees and angle of depression of its reflection in water (point C) is 60 degrees; height of Chhatri above water level is approximately 10 m] Draw a well-labelled figure based on the above information.
[case context: Gadisar Lake chhatri; from point A at h m above water level, angle of elevation of top of Chhatri (point B) is 45 degrees and angle of depression of its reflection in water (point C) is 60 degrees; height of Chhatri above water level is approximately 10 m] Find the height (h) of the point A above water level. (Use sqrt(3) = 1.73)
The angle of elevation of the top of a building from the foot of the tower is 30 degrees and the angle of elevation of the top of the tower from the foot of the building is 60 degrees. If the tower is 50 m high, then find the height of the building.
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30 degrees and 45 degrees respectively. If the bridge is at a height of 3 m from the banks, then find the width of the river.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 9 Some Applications of Trigonometry?
By how often and how recently they were asked: Heights and distances - two angles / two positions; Heights and distances - single elevation/depression; Heights and distances - two objects (tower + building etc.).
How many marks does Some Applications of Trigonometry carry in the CBSE Class 10 Mathematics (Standard) exam?
Some Applications of Trigonometry is part of the Trigonometry unit, which carries 12 marks in the official syllabus. In the analysed papers it had about 3.1 questions per paper.
Do questions from Some Applications of Trigonometry repeat in board exams?
Yes — 4 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.