Question

The angles of elevation and depression of the top and bottom of a lighthouse from the top of a 60 m high building are ${30}^o$ and ${60}^o$ , respectively. Find the difference between the heights of the lighthouse and building.

Answer 1

$\tan 60=\frac{h}{b}$

$\sqrt{3}=\frac{60}{b}$

$b=\frac{60}{\sqrt{3}}=20\sqrt{3}$

$\tan 30=\frac{h}{b}$

$\frac{1}{\sqrt{3}}=\frac{h}{20\sqrt{3}}$

$h=20$