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NDA 2020 Maths · Mathematics · Heights and Distances · medium

From the top of a building 30 m high, the angle of depression of the foot of a tower is 60^° and the angle of elevation of the top of the tower is…

Single correct option

From the top of a building 3030 m high, the angle of depression of the foot of a tower is 60∘60^\circ and the angle of elevation of the top of the tower is 30∘30^\circ. The height of the tower is
  1. A. 3030 m
  2. B. 3535 m
  3. C. 4040 m
  4. D. 30330\sqrt3 m
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Answer: (C) 4040 m

The horizontal distance is d=30tan⁡60∘=103d=\dfrac{30}{\tan60^\circ}=10\sqrt3 m. The top of the tower is dtan⁡30∘=103⋅13=10d\tan30^\circ=10\sqrt3\cdot\frac1{\sqrt3}=10 m above the building top, so the tower height is 30+10=4030+10=40 m. Using only the 1010 m rise forgets the tower foot is at ground level.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake