Question:
Find the angle of elevation of the sun when the shadow of a pole h m high is √3 h m long.
Solution:
Let the angle of elevation of the sun is θ.
Given, height of pole = h
Now, in $\triangle A B C$,
$\tan \theta=\frac{A B}{B C}=\frac{h}{\sqrt{3} h}$
$\Rightarrow$ $\tan \theta=\frac{1}{\sqrt{3}}=\tan 30^{\circ} \Rightarrow \theta=30^{\circ}$
Hence, the angle of elevation of the Sun is $30^{\circ}$.