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°
(b) 30°
(c) 60°
(d) 90°

Answer 1

(b) 30°

Let $AB$ be the pole and $BC$ be its shadow.



Let $AB=h$ and $BC=x$ such that $x=\sqrt{3}h$ (given) and $\theta$ be the angle of elevation.
From ∆$ABC$, we have:
$\frac{AB}{BC}=\tan \theta$

⇒ $\frac{h}{x}=\frac{h}{\sqrt{3}h}=\tan \theta$
⇒ $\tan \theta =\frac{1}{\sqrt{3}}$
⇒ $\theta ={30}^{\mathrm{o}}$

Hence, the angle of elevation is ${30}^{\mathrm{o}}$.