Question

The angle of elevation of the top of a pillar at a distance of 18 m from its foot is 30°. Find the height of the pillar.

Answer 1

Let $AB$ be the pillar, $C$ be the foot of the person such that $BC=18$ m. Thus, we have:
∠$ACB={30}^{\mathrm{o}}$

From right ∆$ABC$, we have:
$\frac{AB}{BC}=\tan {30}^{\mathrm{o}}=\frac{1}{\sqrt{3}}$
⇒ $\frac{h}{18}=\frac{1}{\sqrt{3}}$
⇒ $h=\frac{18}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{18\sqrt{3}}{3}=6\sqrt{3}$ m
∴ Height of the tower = $AB=h=6\sqrt{3}$ m