Find the angle of elevation of the Sun, when the length of the shadow of a tree is 1/√ 3 times the height of the tree.

The correct option is 60^◦.

Let us represent the height of the tree as $h$ and the length of the shadow of the tree as $s$.

According to the given problem statement, the length of the shadow is $\frac{1}{\sqrt{3}}$ times the height of the tree. Therefore, we can write the relationship as:

$s=\frac{1}{\sqrt{3}}\times h$

This can also be rewritten to express the ratio of the height to the shadow length:

$\frac{h}{s}=\sqrt{3}$

Let $\theta$ be the angle of elevation of the Sun. In a right-angled triangle formed by the tree, its shadow on the ground, and the line of sight to the Sun, the tangent of the angle of elevation ($\tan \theta$) is defined as the ratio of the opposite side (height of the tree, $h$) to the adjacent side (length of the shadow, $s$):

$\tan \left(\theta \right)=\frac{h}{s}$

By substituting the ratio we found earlier into this trigonometric equation, we get:

$\tan \left(\theta \right)=\sqrt{3}$

We know from standard trigonometric values that the tangent of 60^◦ is equal to $\sqrt{3}$:

$\tan \left({60}^{◦}\right)=\sqrt{3}$

Comparing the two equations, we find:

$\theta ={60}^{◦}$

Thus, the angle of elevation of the Sun is 60^◦.