Question

From a light house the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the light house is h metres, the distance between the ships is

(a) $\left(\sqrt{3}+1\right)h\mathit{}metres$

(b) $\left(\sqrt{3}-1\right)h\mathit{}metres$

(c) $\sqrt{3}h\mathit{}metres$

(d) $1+\left(1+\frac{1}{\sqrt{3}}\right)hmetres$

Answer 1

Let the height of the light house AB be meters

Given that: angle of depression of ship are and.

Distance of the ship C = and distance of the ship D =

Here, we have to find distance between the ships.

So we use trigonometric ratios.

In a triangle,

Again in a triangle ABD,

Now, distance between the ships

Hence the correct option is .