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NDA 2016 Maths · Mathematics · Heights and Distances · medium

From the top of a lighthouse 75 m high, the angles of depression of two ships on opposite sides of the lighthouse are 30^° and 45^°. The distance…

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From the top of a lighthouse 7575 m high, the angles of depression of two ships on opposite sides of the lighthouse are 30∘30^\circ and 45∘45^\circ. The distance between the ships (in m) is
  1. A. 75(3−1)75(\sqrt3-1)
  2. B. 150150
  3. C. 75375\sqrt3
  4. D. 75(3+1)75(\sqrt3+1)
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Answer: (D) 75(3+1)75(\sqrt3+1)

The ships are at distances 75cot⁡30∘=75375\cot30^\circ=75\sqrt3 m and 75cot⁡45∘=7575\cot45^\circ=75 m from the foot. They are on opposite sides, so the distances add: 753+75=75(3+1)75\sqrt3+75=75(\sqrt3+1). Subtracting would apply only when both ships are on the same side.
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Original question written in the NDA 2016 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