Question

The angles of depression of two ships from the top of a light house are 45° and 30° towards east. If the ships are 100 m apart. the height of the light house is

(a) $\frac{50}{\sqrt{3+1}}m$

(b) $\frac{50}{\sqrt{3-1}}m$

(c) $50\left(\sqrt{3}-1\right)m$

(d) $50\left(\sqrt{3}+1\right)m$

Answer 1

Let = be the light house.

The given situation can be represented as,

It is clear that and

Again, let and m is given.

Here, we have to find the height of light house.

So we use trigonometric ratios.

In a triangle,

Again in a triangle ABD,,

Put

Hence the correct option is .