Height & Distance

Ladakh Prison Department · Mathematics · 32 practice questions with answers and explanations: 13 Easy, 15 Medium, 4 Hard.

Sample questions

Sample Easy question 1

The angle of elevation of the top of a tower from a point 20 m away is 45°. Find the height of the tower.

  1. 20 m
  2. 18 m
  3. 15 m
  4. 25 m
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Answer: A. Height = distance × tan(45°) = 20 × 1 = 20 m.

Sample Easy question 2

A pole casts a shadow equal in length to its own height. Find the angle of elevation of the sun.

  1. 60°
  2. 30°
  3. 45°
  4. 90°
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Answer: C. When shadow length equals height, tan(angle) = height/shadow = 1, so the angle is 45°.

Sample Easy question 3

A ladder 10 m long rests against a wall, making a 30° angle with the ground. Find the height it reaches on the wall.

  1. 6 m
  2. 4 m
  3. 7 m
  4. 5 m
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Answer: D. Height = ladder length × sin(30°) = 10 × 0.5 = 5 m.

Sample Medium question 4

A tower's height is 30 m. Find the angle of elevation of its top from a point 30√3 m away.

  1. 60°
  2. 45°
  3. 30°
  4. 90°
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Answer: C. tan(angle) = height/distance = 30/(30√3) = 1/√3, so the angle is 30°.

Sample Medium question 5

The angle of depression from the top of a cliff to a boat is 45°. If the cliff is 35 m tall, find the distance of the boat from the base of the cliff.

  1. 40 m
  2. 35 m
  3. 32.5 m
  4. 30 m
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Answer: B. The angle of depression equals the angle of elevation from the boat; distance = height/tan(45°) = 35/1 = 35 m.

Sample Medium question 6

The angle of depression from the top of a 50 m tall building to a car is 30°. Find the distance of the car from the base (take √3 = 1.73).

  1. 88 m
  2. 82.5 m
  3. 90 m
  4. 86.5 m
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Answer: D. Distance = height / tan(30°) = 50 × √3 = 50 × 1.73 = 86.5 m.

Sample Hard question 7

The angles of elevation of the top of a tower from two points 40 m apart on the same side, both in line with the base, are 30° and 60°. Find the height of the tower (take √3 = 1.73).

  1. 32.6 m
  2. 33.6 m
  3. 35.6 m
  4. 34.6 m
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Answer: D. Height = d / (cot30° - cot60°) = 40 / (√3 - 1/√3) = 40 / (2/√3) = 20√3 ≈ 34.6 m.

Sample Hard question 8

A vertical pole and a tower stand on the same level ground. The angle of elevation of the top of the tower from the foot of the pole is 60°, and the angle of elevation of the top of the pole from the foot of the tower is 30°. If the pole is 15 m tall, find the height of the tower.

  1. 50 m
  2. 45 m
  3. 40 m
  4. 48 m
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Answer: B. Let the distance between them be d. Pole: 15 = d×tan(30°), so d = 15√3. Tower: height = d×tan(60°) = 15√3 × √3 = 45 m.

Sample Hard question 9

The angle of elevation of a tower's top changes from 30° to 60° as an observer moves 40 m closer. Find the height of the tower.

  1. 28.3 m
  2. 34.6 m
  3. 40 m
  4. 20 m
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Answer: B. Using h = d/(cot30° - cot60°) = 40/(√3 - 1/√3) = 20√3 ≈ 34.6 m.

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