Question

From the top of a light house, the angles of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light house be h metres and the line joining the ships passes through the foot of the light house, show that the distance between the ship is

$\frac{h\left(\tan \alpha +\tan \beta \right)}{\tan \alpha +\tan \beta }$ metres.

Answer 1

Let be the height of light house. And an angle of depression of the top of light house from two ships are and respectively. Let, . And , .

We have to find distance between the ships

We have the corresponding figure as follows

We use trigonometric ratios.

In

Again in

Now,

Hence the distance between ships is .