A light house tower is 150m high from sea level the angle of depression from the tower to the ship is 60 degree.find the distance between the ship and tower?

Drawing a picture can help you see how to set this up. Your picture will be of a right angle triangle, where you can label the distance from the boat to the tower as "x" and the height of the tower is 150m. Now draw the hypotenuse from the top of the tower to the boat. The angle between the horizontal and the hypotenuse is 60 degrees (I assume that's what "angle of depression" means). Now apply the definition of the tangent:

tan(60) = 150/x (this is from knowing that the tangent of an angle is the length of the opposite leg over the adjacent leg).

and solve for x.