Height & Distance

Ladakh Police Sub-Inspector · Mathematics · 32 practice questions with answers and explanations: 13 Easy, 15 Medium, 4 Hard.

Sample questions

Sample Easy question 1

A ladder 12 m long rests against a wall, making a 30° angle with the ground. Find the height it reaches on the wall.

  1. 5 m
  2. 7 m
  3. 8 m
  4. 6 m
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Answer: D. Height = ladder length × sin(30°) = 12 × 0.5 = 6 m.

Sample Easy question 2

As a person walks away from a tower, what generally happens to the angle of elevation of the tower's top?

  1. It stays the same
  2. It becomes 90°
  3. It increases
  4. It decreases
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Answer: D. As distance from the base increases, the angle of elevation decreases.

Sample Easy question 3

As a person walks toward a tower, what generally happens to the angle of elevation of the tower's top?

  1. It decreases
  2. It increases
  3. It stays the same
  4. It becomes 0°
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Answer: B. As distance from the base decreases, the angle of elevation increases.

Sample Medium question 4

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 Medium question 5

Two poles of equal height stand on either side of a 20 m wide road. From the midpoint, the angle of elevation of one pole is 30°. Find the height of the pole.

  1. 5.77 m
  2. 6.5 m
  3. 5 m
  4. 7 m
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Answer: A. Distance from midpoint to pole = 10 m. Height = 10 × tan(30°) = 10/√3 ≈ 5.77 m.

Sample Medium question 6

From a point, the angle of elevation of a tower's top is 60°. Moving 20 m farther away (directly in line with the base), the angle of elevation becomes 30°. Find the height of the tower (take √3 = 1.73).

  1. 16.3 m
  2. 18.3 m
  3. 15.3 m
  4. 17.3 m
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Answer: D. Height = d / (cot30° − cot60°) = 20 / (√3 − 1/√3) = 10√3 ≈ 17.3 m.

Sample Hard question 7

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.

Sample Hard question 8

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 9

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.

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