The angle of elevation of the top of a tower from a point on ground which is 30 mtrs. away from the foot of the tower is 30°. Height of the tower is:

Solution

Here, AB is the height of the tower.
BC is the distance between the foot of the tower and the point.
$$tan 30^\circ = \dfrac{AB}{30}$$

=> $$\dfrac{1}{\sqrt{3}}= \dfrac{AB}{30}$$

=> $$AB = \dfrac{30}{\sqrt{3}}$$

=> $$AB = \dfrac{30}{\sqrt{3}}\times\dfrac{\sqrt{3}}{\sqrt{3}}$$
$$= 10\sqrt{3} m$$