Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flagstaff are respectively 60° and 45°. Find the height of the flag-staff and that of the tower.

Answer 1

Let BC be the tower of height x m and AB be the flag staff of height y, 70 m away from the tower, makes an angle of elevation are 60° and 45° respectively from top and bottom of the flag staff.

Let AB = y m, BC = x m and CD = 70 m.

and

So we use trigonometric ratios.

In a triangle,

Again in a triangle,

Hence the height of flag staff is m and height of tower is m.