Question

If the height of a vertical pole is $\sqrt{3}$ times the length of its shadow on the ground then the angle of elevation of the sun at that time is

(a) ${30}^{\circ }$

(b) ${45}^{\circ }$

(c) ${60}^{\circ }$

(d) ${75}^{\circ }$

Answer 1

Consider the height of the tower be h

∴ the height of shadow $=\sqrt{3}h$

In a triangle ABC,

$tan\angle ACB=\frac{h}{\sqrt{3}h}$

$tan\angle ACB=\frac{1}{\sqrt{3}}$

$\angle ACB={30}^o$

Therefore, the angle of elevation is ${30}^o$