Let $h$ represent the height of the pole and $s = \sqrt{3}h$ represent the length of its shadow. Let $\theta$ denote the angle of elevation of the Sun. Considering the right triangle formed by the pole and its shadow, we have:\[\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{\sqrt{3}h} = \frac{1}{\sqrt{3}}\]Referencing standard trigonometric values, we find:\[\tan 30° = \frac{1}{\sqrt{3}} \implies \theta = 30°\]