Question

A vertical pole is fixed on a tower which is 30m high. From a point on the ground, the angles of elevation of the bottom and the top of the pole are ${45}^{\circ }$ and ${60}^{\circ }$ respectively. Find the height of the pole.

• A. 30 m
• B. 15$\sqrt{3}$ m
• C. 30($\sqrt{3}$ - 1) m
• D. 60 m

Answer 1

The correct option is C

30($\sqrt{3}$ - 1) m

BC = 30m

Let CD = x

In $\Delta$ABC

AB = BC = 30m

In $\Delta$ABD

BD = AB$\sqrt{3}$ = 30$\sqrt{3}$

Hence, height of pole = CD = BD – BC = 30($\sqrt{3}$-1)m