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) $(\sqrt{3} + 1) h m e t r e s$

(b) $(\sqrt{3} - 1) h m e t r e s$

(c) $\sqrt{3} h m e t r e s$

(d) $1 + (1 + \frac{1}{\sqrt{3}}) h m e t r e s$

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Solution

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 .

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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) 3+ 1 h metres (b) 3- 1 h metres (c) 3 h metres (d) 1 + 1+13 h metres