From a ship two lighthouse bears N40°E .after the ship traveled 15.0 miles, on a course of 135° they bear 10° and 345° respectively. Find the distance between them and the distance from the ship in the latter to the more distant lighthouse..
Draw a careful diagram, keeping track of all the angles. If I have done mine right, then if we let
S = original ship location
T = new ship location
A = nearer lighthouse
B = farther lighthouse
ST = 15
SA/sin30° = 15/sin55°
SB/sin55° = 15/sin40°