NDA 2023 Maths · Mathematics · Heights and Distances · hard

A flagstaff 10 m long stands on top of a vertical tower. From a point on the level ground the angles of elevation of the bottom and the top of the…

Single correct option

A flagstaff

10

m long stands on top of a vertical tower. From a point on the level ground the angles of elevation of the bottom and the top of the flagstaff are

30^\circ

and

60^\circ

respectively. The height of the tower is

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Answer: (A) $5$ m

Let the tower have height

H

and the point be at distance

d

from its foot. Then

H=d\tan30^\circ=\frac d{\sqrt3}

and

H+10=d\tan60^\circ=d\sqrt3

. Subtracting,

10=d\left(\sqrt3-\frac1{\sqrt3}\right)=\frac{2d}{\sqrt3}

, so

d=5\sqrt3

and

H=5

m. Taking

d

as the answer is the trap.

Original question written in the NDA 2023 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