Question

An observer on the top of a lighthouse observes the angles of depression of two ship at anchor to be 75 and 45 respectively. Find the distance between the two ships if the line joining them points to the base of the light house which is 100 meters high. (use tan 15 = 0.27) Answer should be 73 meter.

Answer 1

Distance between two ships = 73 units

Explanation:

Note:

tangent = opposite / hypotenuse

Referring to diagram,

Distance of ship A from tower = 100 tan(90-45) = 100 units

Distance of ship B from tower = 100 tan(90-75) = 100 tan (27) = 27 units

Distance between two ships = 100-27 = 73 units