CBSE Class 10 Mathematics (Basic) 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)
- 6 question patterns repeated across papers
Important topics in Some Applications of Trigonometry
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Heights and distances - single elevation/depression | Board 2023Board 2025Board 2026 | ★★★☆☆ |
| 2 | Heights and distances - two objects (tower + building etc.) | Board 2023Board 2024Sample 2025Sample 2026 | ★☆☆☆☆ |
| 3 | Heights and distances - two angles / two positions | Board 2022Board 2023Board 2024Sample 2025 | ★☆☆☆☆ |
Repeated questions from Some Applications of Trigonometry
1. Ladder length via sine
4×Board 2025Board 20261/2 marks
[Case: An injured bird is on the roof of a 15 m high building; a fireman uses an adjustable ladder placed at 60° with the ground to reach the roof.] Find the length of the ladder used by the fireman to reach the roof.
2. Ground distance via tangent
4×Board 2025Board 20261/2 marks
[Case: An injured bird is on the roof of a 15 m high building; a fireman uses an adjustable ladder placed at 60° with the ground to reach the roof.] Find the distance of the point on the ground at which the ladder was fixed from the bottom of the building.
3. Two points, find tower height
4×Board 2022Board 2023Board 2024Sample 20252/5 marks
As observed from the top of a 75 m high lighthouse from the sea level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use √3 = 1.732)
4. Elevation of top + depression of foot
2×Sample 2025Sample 20265 marks
The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°. If the height of the tower is 40 meters, find the height of the chimney. Also, find the length of the wire tied from the top of the chimney to the top of tower.
5. Two depression angles to a building
2×Board 2024Sample 20265 marks
The angles of depression of the top and bottom of a 50m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building. (Use √3 = 1.73)
6. Identify angle of depression
2×Board 2025Board 20261 marks
In the given figure, which of the following angles represents the angle of depression ? [Observer at top with horizontal line; line of sight to Object; marked angles x, y, z at observer/horizontal and a at object] (A) x (B) y (C) z (D) a
Some Applications of Trigonometry questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 3 | 7 |
| Board 2023 | 3 | 11 |
| Board 2024 | 2 | 10 |
| Board 2025 | 5 | 7 |
| Sample 2025 | 2 | 10 |
| Board 2026 | 5 | 7 |
| Sample 2026 | 2 | 10 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Some Applications of Trigonometry
Board 2026 5 questions
In the given figure, which of the following angles represents the angle of depression ? [Observer at top with horizontal line; line of sight to Object; marked angles x, y, z at observer/horizontal and a at object] (A) x (B) y (C) z (D) a
[Case: An injured bird is on the roof of a 15 m high building; a fireman uses an adjustable ladder placed at 60° with the ground to reach the roof.] Find the length of the ladder used by the fireman to reach the roof.
[Case: An injured bird is on the roof of a 15 m high building; a fireman uses an adjustable ladder placed at 60° with the ground to reach the roof.] Find the distance of the point on the ground at which the ladder was fixed from the bottom of the building.
[Case: An injured bird is on the roof of a 15 m high building; a fireman uses an adjustable ladder placed at 60° with the ground to reach the roof.] In order to avoid skidding, the fireman placed the ladder in such a way that the bottom of the ladder touches the base of the wall which is opposite to the building, making an angle of 30° with the ground. Draw a neat diagram to represent the above situation and hence find the width of the road between the building and the wall.
[Case: An injured bird is on the roof of a 15 m high building; a fireman uses an adjustable ladder placed at 60° with the ground to reach the roof.] The fireman placed the ladder from the base of the opposite wall making an angle of 30° with the ground. Find the length of the ladder used by the fireman in this case.
Sample 2026 2 questions
The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°. If the height of the tower is 40 meters, find the height of the chimney. Also, find the length of the wire tied from the top of the chimney to the top of tower.
The angles of depression of the top and bottom of a 50m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building. (Use √3 = 1.73)
Board 2025 5 questions
In the given figure, which of the following angles represents the angle of depression ? (Observer at top, horizontal line, line of sight to object; angles labelled z, y at observer, a and x at object.) (A) x (B) y (C) z (D) a
[Case context: An injured bird is on the roof of a 15 m high building; a fireman uses an adjustable ladder making 60° with the ground to reach the roof.] Find the length of the ladder used by the fireman to reach the roof.
[Case context: An injured bird is on the roof of a 15 m high building; a fireman uses an adjustable ladder making 60° with the ground to reach the roof.] Find the distance of the point on the ground at which the ladder was fixed from the bottom of the building.
[Case context: 15 m high building, fireman's ladder.] In order to avoid skidding, the fireman placed the ladder in such a way that the bottom of the ladder touches the base of the wall which is opposite to the building, making an angle of 30° with the ground. Draw a neat diagram to represent the above situation and hence find the width of the road between the building and the wall.
[Case context: 15 m high building, fireman's ladder now making 30° with the ground from the base of the opposite wall.] Find the length of the ladder used by the fireman in this case.
Sample 2025 2 questions
From the top of a 9 m high building, the angle of elevation of the top of a cable tower is 60° and angle of depression of its foot is 45°. Determine the height of the tower and distance between building and tower. (Use √3 = 1.732)
As observed from the top of a 75 m high lighthouse from the sea level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use √3 = 1.732)
Board 2024 2 questions
The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it was 60°. Find the height of the tower and the length of original shadow. (use √3 = 1.73)
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. (use √3 = 1.73)
Board 2023 3 questions
The angle subtended by a vertical pole of height 100 m at a point on the ground 100√3 m from the base is, has measure of : (a) 90° (b) 60° (c) 45° (d) 30°
A TV tower stands vertically on the bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from the point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower.
An aeroplane when flying at a height of 4000 m from the ground passes vertically above another aeroplane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the aeroplanes at that instant. (Use √3 = 1.73)
Board 2022 3 questions
[Case context: A TV Tower stands vertically on the ground; from a point A on the ground the angle of elevation of the top B is 60 degrees, and a point C on the tower 78 m above the ground has an angle of elevation of 30 degrees from A.] Draw a well-labelled figure, based on the information given above.
[Case context: A TV Tower stands vertically on the ground; from a point A on the ground the angle of elevation of the top B is 60 degrees, and a point C on the tower 78 m above the ground has an angle of elevation of 30 degrees from A.] Find the height of the tower and the distance of the tower from point A.
In Figure 2, the angles of elevation of the top of a tower AB of height 'h' m, from two points P and Q at a distance of x m and y m from the base of the tower respectively and in the same straight line with it, are 60 degrees and 30 degrees, respectively. Prove that h2 = xy.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) Chapter 9 Some Applications of Trigonometry?
By how often and how recently they were asked: Heights and distances - single elevation/depression; Heights and distances - two objects (tower + building etc.); Heights and distances - two angles / two positions.
How many marks does Some Applications of Trigonometry carry in the CBSE Class 10 Mathematics (Basic) 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 — 6 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.