Height & Distance

LSSSSB Non-Technical · 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

From a point on the ground, the angle of elevation of a 20 m tower's top is 30°. Find the distance of the point from the base.

  1. 40 m
  2. 34.6 m
  3. 28.5 m
  4. 30 m
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Answer: B. Distance = height/tan 30° = 20 × √3 ≈ 34.6 m.

Sample Medium question 5

From the top of a 60 m tower, the angle of depression to a car is 30°. Find the distance of the car from the base of the tower.

  1. 96 m
  2. 103.9 m
  3. 110 m
  4. 90 m
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Answer: B. Distance = 60/tan 30° = 60√3 ≈ 103.9 m.

Sample Medium question 6

A tower's shadow is 30 m long when the angle of elevation of the sun is 30°. Find the height of the tower.

  1. 15 m
  2. 20 m
  3. 17.3 m
  4. 25 m
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Answer: C. Height = 30 × tan 30° = 30/√3 ≈ 17.3 m.

Sample Hard question 7

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 8

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.

Sample Hard question 9

From a point 60 m above a lake, the angle of elevation of a cloud is 30° and the angle of depression of its reflection is 60°. Find the height of the cloud above the lake.

  1. 150 m
  2. 195 m
  3. 165 m
  4. 180 m
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Answer: D. Solving the standard cloud-reflection formula gives a height of 120 m above the observer, i.e. 60+120 = 180 m above the lake.

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