Question

A tower subtends a right angle at the top of the hillock and the angle of elevation of the top of the hillock from the bottom of tower is 60

Answer 1

The height of the tower is $8\sqrt{3}$m

Step-by-step explanation:

Assuming that the distance between the tower and the hillock is 6m

and

we have to find the height of the tower

let AB be the height of the tower and CD be the height of the hillock

then,

$\angle ACE$= 90° and ED = 6 m

In $\bigtriangleup CED$

Tan 60° = $\frac{CD}{ED}$

$\sqrt{3} = \frac{CD}{ED}$

CD= BE = $6\sqrt{3}$

In traingle ABC

tan 30° = $\frac{AB}{BC}$

using BC = 6m

AB = $2\sqrt{3}$

and the height of the tower = AB+ BE

= $6\sqrt{3}+2\sqrt{3}$

= $8\sqrt{3}$

hence ,

The height of the tower is $8\sqrt{3}$m

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