PrepRung
Sign inSign up free

NDA 2016 Maths · Mathematics · Heights and Distances · hard

A flagstaff stands on top of a tower 20 m high. From a point on the ground 20 m from the foot of the tower, the angle of elevation of the top of the…

Single correct option

A flagstaff stands on top of a tower 2020 m high. From a point on the ground 2020 m from the foot of the tower, the angle of elevation of the top of the flagstaff is 60∘60^\circ. The length of the flagstaff (in m) is
  1. A. 20(3−1)20(\sqrt3-1)
  2. B. 20320\sqrt3
  3. C. 20(3+1)20(\sqrt3+1)
  4. D. 203\dfrac{20}{\sqrt3}
Show answer and solution

Answer: (A) 20(3−1)20(\sqrt3-1)

The top of the flagstaff is at height 20tan⁡60∘=20320\tan60^\circ=20\sqrt3 m. The tower top is at 2020 m (the tower itself subtends 45∘45^\circ). Hence the flagstaff has length 203−20=20(3−1)20\sqrt3-20=20(\sqrt3-1). The value 20320\sqrt3 is the total height of tower plus flagstaff.
Report a mistake

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