Question

as observed from the top of a 100m high light house from sealevel the angles of depression of two ships are 30 to 40°.if one ship is exactly behind the other on the same side of the lighthouse .find the distance between the two ships.

Answer 1

Let AB is the light house. So AB = 75

From triangle ABC,

tan 45 = AB/BC

=> 1 = 75/BC

=> BC = 75

Again from triangle ADC

tan30 = AB/BD

=> 1/√3 = AB/(BC + CD) 

=> 1/√3 = 75/(75 + CD)

=> 1/√3 = 75/(75 + CD)

=> 75 + CD = 75√3

=> CD = 75√3 - 75

=> CD = 75(√3 - 1)
so, the distance between two ship is 75(√3-1)m