Question

From a point on the ground which is at a distance of $50m$ from the foot of the tower, the angle of elevation of the top of the tower is observed to be 30${}^{\circ }.$ Find the height of the tower.

Answer 1

Let the height of the tower be $hm$
$\Rightarrow AB=h$

From $△PAB,$

$\tan {30}^{\circ }=\frac{AB}{PA}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{50}$

$\Rightarrow h=\frac{50}{\sqrt{3}}$

Hence, the height of the tower is $\frac{50}{\sqrt{3}}$ $m$