Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are respectively ${30}^{\circ }and{60}^{\circ }$ . Find the height of the tower.

Answer 1

Let h be the height of the tower.

In right ΔDBC,

$tan30=\frac{DB}{BC}$

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

$x=\sqrt{3}h$

In right ΔABC,

$tan60=\frac{AB}{BC}$

$3h=h+5$

$h=2.5m$

Thus, height of the tower = 2.5 m