Question

From the top of $20$ metres high light house, the angle of depression of the ship of ${30}^{\circ }$. Find the distance between the ship and light house.

Answer 1

Let $AB$ is a $20M$ high light-house and a ship is at the point $C$.

According to the question

$AB=20m,\angle DBC=\angle ACB={30}^{\circ }$

In $△ABC$

$\tan {30}^{\circ }=\frac{AB}{AC}$

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

$x=20\sqrt{3}$

$x=20\times 1.732$

$x=34.64metres$

So, the distance between lighthouse and ship is $34.64meters$.