Question

If the height of a pole is $2\sqrt{3}$ metres and the length of its shadow is $2$ metres, find the angle of elevation of the sun.

Answer 1

Let $AB$ be the pole and $AC$ be its shadow, as shown in the above figure.

Let angle of elevation, $\angle ACB=\theta$

Then, $AB=2\sqrt{3}m$ and $AC=2m$

$\tan \theta =\frac{AB}{AC}=\frac{2\sqrt{3}}{2}=\sqrt{3}$

Since, $\tan \theta =\sqrt{3},\theta ={60}^{\circ }$

So, the angle of elevation is ${60}^{\circ }$.