NDA 2021 Maths · Mathematics · Heights and Distances · hard

The angles of elevation of the top of a tower from two points on a line through its foot, at distances 9 m and 16 m from it, are complementary.

Single correct option

The angles of elevation of the top of a tower from two points on a line through its foot, at distances

9

m and

16

m from it, are complementary. The height of the tower is

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Answer: (C) $12$ m

If the angles are

\alpha

and

90^\circ-\alpha

, then

\tan\alpha=\dfrac h9

and

\cot\alpha=\dfrac h{16}

. Multiplying,

\dfrac{h^2}{144}=1

, so

h=12

m (the geometric mean of 9 and 16).

Original question written in the NDA 2021 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