Question

On a horizontal plane, there is a vertical tower with a flagpole on the top of the tower. At a point 9 meters away from the foot of the tower the angle of elevation of the top and bottom of the flagpole are 60° and 30° respectively. Find the height of the tower and the flagpole mounted on it.

Answer 1

Let AB be the tower of height h and AD be the flagpole on the tower. At the point 9m away from the foot of the tower, the angle of elevation of the top and bottom of the flagpole is 60° and 30°

Let AD = x, BC = 9 and ∠ACB = 30°, ∠DCB = 60°

Here we have to find the height of tower and height of the flagpole.

The corresponding diagram is as follows

In a triangle ABC,

`=> tan C = (AB)/(BC)`

`=> tan 30^@ = h/9`

`=> 1/sqrt3 = h/9`

`=>h = 9/sqrt3`

`=> h = 3sqrt3`

Again in a triangle DBC

`=> tan C = (AD + AB)/(BC)`

`=> tan 60^@ = (h + x)/9`

`=> sqrt3 = (h + x)/9`

`=> 9sqrt3 = h + x`

`=> 9sqrt3 = 3sqrt3 + x`

`=> x = 6sqrt3`

So height of tower is `3sqrt3` meter and height of flag pole is `6sqrt3` meters