Question

A tower subtends a right angle at the top of the hillock and the angle of elevation of the top of the hillock from the bottom of the tower is ${60}^{\circ }$. If the distance between the tower and the hillock is $6m$, then the height of the tower is-

• A. $2\sqrt{3}$m
• B. $4\sqrt{3}$m
• C. $\sqrt{3}$m
• D. $8\sqrt{3}$m

Answer 1

The correct option is D $8\sqrt{3}$m

Let $AE$ be the height of tower and $CD$ be the height of hillock. Then $\angle ACE={90}^o$ and $ED=6m$

In $△CED\tan {60}^o=\frac{CD}{ED}=\sqrt{3}$

$\Rightarrow CD=6\sqrt{3}=BE$

and In $△ABC\tan {30}^o=\frac{AB}{BC}$

and $BC=6m\therefore AB=2\sqrt{3}$

and Height of tower $=AB+BE=6\sqrt{3}+2\sqrt{3}$

$=8\sqrt{3}m$