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 ${30}^{\circ }$. Find the height of the tower.

• A. 10√3 m
• B. 20√3 m
• C. 30√3 m
• D. 20m

Answer 1

The correct option is A

10√3 m

$\text{Angle of elevation}=\theta ={30}^{\circ }$
$\Rightarrow \tan \theta =\frac{P}{B}$
$\Rightarrow \tan \theta =\frac{h}{30}$
$\Rightarrow \tan {30}^{\circ }=\frac{1}{\sqrt{3}}$
$\Rightarrow \frac{h}{30}=\frac{1}{\sqrt{3}}$
$\therefore h=10\sqrt{3}m$.