Question

From a point on the ground, 30 m away from the foot of a tower, the angle of elevation of the top of the tower is ${30}^{\circ }$. The height of the tower is

(a) 30 m

(b) $10\sqrt{3}m$

(c) 10 m

(d) $30\sqrt{3}m$

Answer 1

Let h m be the height of the tower

$In△ABC,$

$tan\theta =\frac{Oppositeside}{Adjacentside}\Rightarrow tan{30}^o=\frac{H}{30}\Rightarrow \frac{1}{\sqrt{3}}=\frac{H}{30}\Rightarrow H=\frac{30}{\sqrt{3}}=\frac{30\sqrt{3}}{3}=10\sqrt{3}m$