Height & Distance

Ladakh Police Constable · 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

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 Medium question 5

From two points 20 m apart in line with a tower's base, the angles of elevation of its top are 30° and 45°. Find the tower's height.

  1. 27.3 m
  2. 25.3 m
  3. 31.3 m
  4. 29.3 m
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Answer: A. Solving h/(h) = 1 and h/(h+20) = 1/√3 gives h = 20/(√3-1) = 10(√3+1) ≈ 27.3 m.

Sample Medium question 6

A kite flies at a height of 60 m, attached to a string inclined at 30° to the horizontal. Find the length of the string.

  1. 120 m
  2. 100 m
  3. 130 m
  4. 110 m
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Answer: A. Length = 60/sin 30° = 60/0.5 = 120 m.

Sample Hard question 7

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 8

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 9

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.

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