Question:
If the ratio of the height of a tower and the length of its shadow is $\sqrt{3}: 1$, what is the angle of elevation of the Sun?
Solution:
Let be the angle of elevation of sun is.
Given that: Height of tower is meters and length of shadow is 1.
Here we have to find angle of elevation of sun.
In a triangle,
$\Rightarrow \tan \theta=\frac{A B}{B C}$
$\Rightarrow \tan \theta=\frac{\sqrt{3}}{1}\left[\because \tan 60^{\circ}=\sqrt{3}\right]$
$\Rightarrow \tan \theta=\sqrt{3}$
$\Rightarrow \theta=60^{\circ}$
Hence the angle of elevation of sun is $60^{\circ} .$