NDA 2023 Maths · Mathematics · Heights and Distances · medium

A tower is 100 m high. Two points on the same side of it, in line with its foot, see the top at elevations 30^° and 60^°. The distance between the…

Single correct option

A tower is

100

m high. Two points on the same side of it, in line with its foot, see the top at elevations

30^\circ

and

60^\circ

. The distance between the points is

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Answer: (B) $\dfrac{200}{\sqrt3}$ m

The distances from the foot are

100\cot30^\circ=100\sqrt3

and

100\cot60^\circ=\dfrac{100}{\sqrt3}

. Since both points lie on the same side, the separation is the difference

100\sqrt3-\dfrac{100}{\sqrt3}=\dfrac{200}{\sqrt3}

m. Adding the distances applies when points are on opposite sides.

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