Question

If the length of the shadow of a tower is $\sqrt{3}$ times its height then the angle of elevation of the sun is

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

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

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

(d) ${90}^{\circ }$

Answer 1

Consider the height of tower be h

∴ height of shadow = $\sqrt{3}\times h$.

In a $△ABC$

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

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

$\angle ACB={30}^{\circ }$

Therefore, angle of elevation is ${30}^{\circ }$