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Class 10 Applications of Trigonometry: 8 practice questions with answers, step by step

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These are 8 practice questions on NCERT Class 10 Maths Chapter 9, Some Applications of Trigonometry (heights and distances), each with a worked answer and the units. They cover the height of a tower from the angle of elevation, a kite string, a ladder, angles of depression, and a two-position problem. Try each one on paper before you open the answer. The ratios used here (tan 30°, tan 45°, tan 60° and the rest) come from the values table of Chapter 8; see our guide to Class 10 Introduction to Trigonometry questions.

These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 9, printed pages 133 to 143):

Angle of elevation

Question 1. From a point on the ground 30 m from the foot of a tower, the angle of elevation of its top is 45°. How tall is the tower, in m?

Answer: 30 m. tan 45° = height ÷ 30 = 1, so the height is 30 m.

Question 2. From a point 10 m from the foot of a tower, the angle of elevation of its top is 60°. How tall is the tower, in m, to one decimal place? (Take √3 = 1.732.)

Answer: 17.3 m. tan 60° = height ÷ 10, so the height = 10 × √3 ≈ 10 × 1.732 = 17.32, which is 17.3 m to one decimal place.

Question 3. A kite string is 60 m long and makes an angle of 30° with the ground. Taking the string as straight, how high is the kite, in m?

Answer: 30 m. The string is the hypotenuse, so height = string × sin 30° = 60 × 1/2 = 30 m.

Question 4. A 10 m ladder leans against a wall and makes an angle of 60° with the ground. How far is its foot from the wall, in m?

Answer: 5 m. The ladder is the hypotenuse and the distance from the wall is the side next to the 60° angle, so distance = 10 × cos 60° = 10 × 1/2 = 5 m. (The textbook's ladder example is on page 136.)

Angle of depression

Question 5. From the top of a 20 m building, the angle of depression of a car on the road is 45°. How far is the car from the foot of the building, in m?

Answer: 20 m. The angle of depression is measured from the horizontal at the top, down to the car (page 134). By alternate angles (the textbook uses the same step in Example 6, pages 139-140) it equals the angle of elevation of the top from the car, so tan 45° = height ÷ distance = 20 ÷ distance = 1, and the distance is 20 m.

Question 6. From the top of a 30 m high tower, the angle of depression of a boat is 30°. How far is the boat from the foot of the tower, in m, to two decimal places? (Take √3 = 1.732.)

Answer: about 51.96 m. tan 30° = 30 ÷ distance = 1/√3, so the distance = 30√3 ≈ 30 × 1.732 = 51.96 m.

Two positions and definitions

Question 7. Standing on flat ground, Meera sees the top of a tower at an angle of elevation of 30°. She walks 20 m straight towards the tower and the angle becomes 60°. How tall is the tower, in m, to one decimal place? (Take √3 = 1.732.)

Answer: 17.3 m. Let the height be h and the nearer distance x. From the second position tan 60° = h/x, so h = √3·x. From the first position tan 30° = h/(x + 20), so √3·h = x + 20. Substituting, 3x = x + 20, so x = 10 m. Then h = 10√3 ≈ 10 × 1.732 = 17.3 m. (Same method as Example 5, pages 138 and 139.)

Question 8. What is the difference between the angle of elevation and the angle of depression of the same two points, A (lower) and B (higher)?

Answer: nothing in size, only the viewpoint. The angle of elevation of B from A is the angle of the line of sight with the horizontal when looking up; the angle of depression of A from B is the angle of the line of sight with the horizontal when looking down. The two horizontals are parallel, so the two angles are equal (alternate angles); that is why questions 5 and 6 can be solved as angles of elevation from the ground. (Definitions, pages 133 and 134; the equal-angles step is used in Example 6, pages 139-140.)

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Sources

All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook.

The definitions and methods are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.