If the shadow of a tree is \(\frac{1}{\sqrt{3}}\) times its height, then angle of elevation of the sun is :

Let the height of the tree be \(h\)

Then, length of the shadow:

\(=\frac{1}{\sqrt{3}}h\)​

Angle of elevation of the sun = \(\theta\)

Using trigonometry:

\(\tan ⁡\theta =\frac{\text{Height of tree}}{\text{Length of shadow}}\)

​ \(\tan ⁡\theta =\frac{h}{\frac{1}{\sqrt{3}}h}\)

​ \(\tan ⁡\theta =\sqrt{3}\)​

We know:

\(\tan ⁡{60}^{∘}=\sqrt{3}\)

​ \(∴\theta ={60}^{∘}\)