Height & Distance

SSC CGL · Quantitative Aptitude · 32 practice questions with answers and explanations: 10 Easy, 10 Medium, 12 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. 6 m
  3. 7 m
  4. 8 m
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Answer: B. Height = ladder length × sin(30°) = 12 × 0.5 = 6 m.

Sample Medium question 2

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

Sample Hard question 3

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

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