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 ${60}^o$ and ${30}^o$ respectively. Find the height of the tower and the flagpole mounted on it.

Answer 1

Let $AB$ be the height of the flagstaff

$BC$ be the height of the Tower

Given that $CD=$ Distance between the foot of the tower and the point $=9$

in $△BDC$

$\tan {30}^o=\frac{BC}{CD}\Rightarrow \frac{1}{\sqrt{3}}=\frac{BC}{9}$

$\Rightarrow BC=3\sqrt{3}=5.19$ $(Take\sqrt{3}=1.73)$

and in $△ACD$

$\tan {60}^o=\frac{AC}{CD}\Rightarrow \sqrt{3}=\frac{AC}{9}$

$\Rightarrow AC=9\sqrt{3}=15.57$ $(Take\sqrt{3}=1.73)$

Hence, height of

FLAGPOLE = $AB=AC-BC=15.37-5.19=10.18m$

TOWER = $5.19m$