The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

Question

A ladder 14 m long just reaches the top of a vertical wall. If the ladder makes an angle of $60^\circ$ with the wall, then the height of the wall is:

Answer 1

The angle of elevation of the top of a tower from a point on the ground
Consider a tower AB. The angle of elevation from a ground point C is 30°.

In right-angled triangle ABC,

$\frac{AB}{ BC} = tan 30°$

Given BC = 30 m, we have:

$\frac{AB}{ 30 }= \frac{1}{ \sqrt3}$

$AB = \frac{30}{ \sqrt3} = 10\sqrt3\,m$

The height of the tower is thus $10\sqrt3\,m$.

Solution and Explanation