Question

The angle of elevation of the top of a tower from a point on the ground, which is $30m$ away from the foot of the tower, is $30°$. Find the height of the tower.

Answer 1

Let $AB$ be the height of the tower

C is the point elevation $=30°$

$BC=30m$

$$\begin{gathered} In△ABC \\ \Rightarrow \tan \left(30°\right)=\frac{AB}{BC} \\ \Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{30} \\ \Rightarrow AB=\frac{30}{\sqrt{3}}m \\ \Rightarrow AB=\frac{30\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}} \\ \Rightarrow AB=10\sqrt{3}m \end{gathered}$$

Hence, the height of the tower is$10\sqrt{3}m$