From a tower of  $80m$height the angle of depression of a bus is  $30°$.  How far is the bus from the tower?

Let  $AC$ be the tower and

$B$ be the position of the bus

$BC=$ The distance of the bus from the foot of the tower

$AC=80m$

$\angle DAB=30°=\angle ABC\left(\therefore DA\left|\right|BC\right)$

$\tan 30°=\frac{AC}{BC}$

$\Rightarrow \tan 30°=\frac{80}{BC}$

$\Rightarrow BC=\frac{80}{\tan 30°}\Rightarrow BC=80\times \frac{\sqrt{3}}{1}=80\sqrt{3}$

$=80\times 1.73$

$\therefore BC=138.4m$