Question

The angle of elevation of the top of a tower from a point A on the ground is ${30}^{\circ }$. On moving a distance of 20 metres towards the foot of the tower to a point B the angle of elevation increases to ${60}^{\circ }$. Find the height of the tower and the distance of the tower from the point A.

Answer 1

Let the height of the tower be h m.

In right ΔDCB,

$tan60=\frac{DC}{CB}$

$\frac{h}{x}=\sqrt{3}$

$x=\frac{h}{\sqrt{3}}$

Again in triangle DCA,

$tan30=\frac{DC}{CA}$

$\frac{1}{\sqrt{3}}=\frac{h}{x+20}$

$h=10\sqrt{3}$

$x=10m$

Thus, distance of tower from point A = x + 20 = 30 m