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 flagstaff 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 flagstaff.

Let AB = y m, BC = x m and CD = 70 m.

So we use trigonometric ratios.

In a triangle BCD

`=> tan D = (BC)/(CD)`

`=> tan 45^@ = x/70`

`=> 1 = 70/x`

`=> x = 70`

Again in a triangle ADC

`=> tan D = (AB + BC)/(CD)`

`=> tan 60^@ = (y + x)/70`

`=> sqrt3 = (y + 70)/70`

`=> 70sqrt3 = 70 + y`

`=> y = 70(sqrt3 - 1)`

=>y = 51.24

Hence the height of flag staff is 51.24 m and height of tower is 70 m