Question

From the top of a 10 m height tree, the angle of depression of a point on the ground is 30°. Then the distance of the point from the foot of the tree is

A) 10 m

B) 10 √3 m

C) 10/√3 m

D) 5 √3 m

Answer 1

Correct option is: B) 10√3 m

In right \(\triangle\)ABC, we have

\(\angle\)CAB = \(30^\circ\) & BC = 10 m

tan A = \(\frac {BC}{AB}\)

= \(\frac {BC}{AB}\) = tan \(30^\circ\) = \(\frac {1}{\sqrt3}\)(\(\because\) \(\angle\)A = \(30^\circ\))

= AB = \(\sqrt3\) BC = 10\(\sqrt3\) m (\(\because\) BC = 10 m)

Hence, the distance of the point from the foot of the tree is 10\(\sqrt3\) m.

Answer 2

Correct option is: B) 10 √3 m