NDA 2025 Maths · Mathematics · Heights and Distances · medium

From two points A and B on level ground, in line with the foot of a tower and on the same side of it, with AB=40 m (A farther), the angles of…

Single correct option

From two points

A

and

B

on level ground, in line with the foot of a tower and on the same side of it, with

AB=40

m (

A

farther), the angles of elevation of the top are

30^\circ

and

60^\circ

respectively. The height of the tower is

Show answer and solution

Answer: (C) $20\sqrt3$ m

Let the height be

h

. Then

h\cot30^\circ-h\cot60^\circ=40

, i.e.

h(\sqrt3-\frac1{\sqrt3})=\frac{2h}{\sqrt3}=40

, so

h=20\sqrt3

m. Writing

AB

as the sum rather than the difference of the distances gives a wrong value.

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