Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 meters. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are respectively 300 and 600. Find the height of the tower.

Answer 1

Let BC be the tower of height, hm and AB be the Flagstaff with distance 5m. Then the angle of elevation from the top and bottom of Flagstaff are 60° and 30° respectively.

Let `CD= x` and `∠ADC = 60^@` ∠BDC = 30°

Here we have to find height h of tower.

So we use trigonometric ratios.

In a triangle BCD

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

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

`=> 1/sqrt3 = h/x`

`=> x =  sqrt3h`

Again in a triangle ACD

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

`=> tan 60^@ = (h + 5)/x`

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

`=> sqrt3x = h + 5` 

`=> sqrt3 xx hsqrt3 = h + 5`

`=> 3h = h + 5`

`=> 2h = 5`

=> h = 2.5

Hence the height of tree is 2.5 m