As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use √3=1.732]

Let, height of light house from sea level (AB) = 100m
Let, two ships be at the positions be C and D
In ΔABC, tan 45° = AB/BC
=> 1 = 100/BC
=> BC = 100m
In ΔABD, tan 30° = AB/BD
=> 1/√3 = AB/BD
BD = AB × √3 = 100 × √3 = 173.2 [√3 = 1.732]
∴ CD = BD - BC = 173.2 - 100 = 73.2m
∴ the distance between two ships 73.2m