The angle of elevation of the top of an unfinished tower at a distance of 75m from its base is 30°. How much higher must the tower be raised so that the angle of elevation of its top at the same point may be 60°?

$50\sqrt{3} m$

The correct answer is Option (2) → $50\sqrt{3} m$

Distance from the tower = 75 m

Initial height of the tower

$h_1 = 75 \tan 30^\circ = 75 \cdot \frac{1}{\sqrt{3}} = 25\sqrt{3}\ \text{m}$

Required final height

$h_2 = 75 \tan 60^\circ = 75\sqrt{3}\ \text{m}$

Extra height required

$h_2 - h_1 = 75\sqrt{3} - 25\sqrt{3} = 50\sqrt{3}\ \text{m}$