A ship is sailing due north. At a certain point the bearing of a lighthouse is N 40∘E and the distance is 15.5. After a while, the captain notices that the bearing of the lighthouse is now S 54.9∘E. How far did the ship travel between the two observations of the lighthouse.

Answer 1

as always, draw a diagram. Label the lighthouse L, and the two ship positions S and N. Draw an E-W line from L to SN, intersecting at P.

SP = 15.5 cos40°
PL = 15.5 sin40°
PN = PL cot54.9°

The ship has sailed a distance of SP+PN