The height of a tree is $\sqrt{3}$ times the length of its shadow. Find the angle of elevation of the sun.

Let AB be the tree and BC be the shadow of tree.

Let the length of the shadow (BC) of the tree be x meters.

So, the height of the tree (AB) = $\sqrt{3}x$ meters.

If θ is the angle of elevation of the sun, then we have :

In △ABC,

$\Rightarrow \text{tan θ} = \dfrac{\text{Perpendicular}}{\text{Base}} \\[1em] \Rightarrow \text{tan θ} = \dfrac{AB}{BC} \\[1em] \Rightarrow \text{tan θ} = \dfrac{\sqrt{3}x}{x} \\[1em] \Rightarrow \text{tan θ} = \sqrt{3} \\[1em] \Rightarrow \text{tan θ} = \text{tan 60°} \\[1em] \Rightarrow θ = 60°.$

Hence, angle of elevation of sun is 60°.