Question

A flag-staff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flag-staff.

Answer 1

Let BC be the tower height of 5 m. flag height is hm and an angle of elevation of the top of the tower is 45° and an angle of elevation of the top of the flag is 60°.

Let AC = hm and BC = 5 m and ∠ADB = 60°, ∠CDB = 45°

We have the corresponding angle as follows

So we use trigonometric ratios.

In a triangle ΔBCD

`=> tan 45^@ = (BC)/(BD)`

`=> 1 = 5/x`

`=> x= 5`

Again in a triangle ABD

`=> tan 60^@ = (AB)/(BD)`

`=> sqrt3 = (5 + h)/5`

`=> h = 5(sqrt3  - 1)`

`=> h = 3.66`

Hence the height of flag is 3.66 m