Question

The angle of elevation of the Sun at an instant when the length of the shadow of a pole is $\sqrt{3}$ times its height, is

• A. 60°
• B. 30°
• C. 15°
• D. 45°

Answer 1

The correct option is B 30°

Let AB be the pole of height h, AC be its shadow and $\alpha$ be the angle of elevation of Sun at an instant.
Given that the length of the shadow of a pole is $\sqrt{3}$ times its height.
⇒ AC = $\sqrt{3}$ h …..(i)
$In\Delta CAB,$
$\tan \alpha =\frac{AB}{AC}$
$\Rightarrow tan\alpha =\frac{h}{\sqrt{3}h}$ [From (i)]
$\Rightarrow tan\alpha =\frac{1}{\sqrt{3}}=tan{30}^o$
$\Rightarrow \alpha ={30}^o$
Hence, the correct answer is option (b).