**Question:**

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

**Solution:**

Let *AB* be the tower of height *h *and *AD* be the flag pole on tower. At the point 9m away from the foot of tower, the angle of elevation of the top and bottom of flag pole are 60° and 30°. Let *AD = x*, *BC* = 9 and, .

Here we have to find height of tower and height of flag pole.

The corresponding diagram is as follows

$\Rightarrow \quad \tan C=\frac{A B}{B C}$

$\Rightarrow \quad \tan 30^{\circ}=\frac{h}{9}$

$\Rightarrow \quad \frac{1}{\sqrt{3}}=\frac{h}{9}$

$\Rightarrow \quad h=\frac{9}{\sqrt{3}}$

$\Rightarrow h=3 \sqrt{3}$

Again in a triangle,

$\Rightarrow \quad \tan C=\frac{A D+A B}{B C}$

$\Rightarrow \tan 60^{\circ}=\frac{h+x}{9}$

$\Rightarrow \quad \sqrt{3}=\frac{h+x}{9}$

$\Rightarrow \quad 9 \sqrt{3}=h+x$

$\Rightarrow \quad 9 \sqrt{3}=3 \sqrt{3}+x$

$\Rightarrow \quad x=6 \sqrt{3}$

So height of tower is $3 \sqrt{3}$ meter and height of flag pole is $6 \sqrt{3}$ meters.

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