Question

A pole $5m$ high is fixed on the top of a tower. The angle of elevation of the top of the pole as observed from a point A on the ground is ${60}^o$ and the angle of depression of the point A from the top of the tower is ${45}^o$. Find the height of the tower.

Answer 1

Given height of the pole, $CD=5m$

Let height of the tower, $BD=h$

$AB=x$

In right $△ABD$

$\tan \theta =\frac{BD}{AB}$

$\tan 45=\frac{h}{x}$

$h=x...\left(1\right)$

Now in right $△ABC$

$\tan 60=\frac{h+5}{h}$

$\sqrt{3}=\frac{h+5}{h}$

$h\sqrt{3}-h=5$

$h(\sqrt{3}-1)=5$

$\therefore h=\frac{5}{\sqrt{3}-1}m$