Find the angle of the elevation of the Sun when the length of shadow of a vertical pole is $\sqrt{3}$ times its height.

Let the height of the vertical pole be $h$.
Then, the length of the shadow is $\sqrt{3}h$.
Let $\theta$ be the angle of elevation of the Sun.

$$\tan \theta =\frac{\text{Height}}{\text{Shadow}}=\frac{h}{\sqrt{3}h}=\frac{1}{\sqrt{3}}$$

We know that $\tan 30^{\circ }=\frac{1}{\sqrt{3}}$.
Therefore, $\theta =30^{\circ }$.