A ship is sailing due north At a certain point the bearing o

A ship is sailing due north. At a certain point the bearing of a lighthouse is N 35E and the distance is 10.5. After a while, the captain notices that the bearing of the lighthouse is now S 50.4E. How far did the ship travel between the two observations of the lighthouse.

Solution

Make a sketch of ABC such that :-

AB is vertical
B is above A and C is to right of AB
A = 35°
B = 50.4°
C = 94.6°
AC = 10.5 km
10.5/ sin50.4 = AB / sin 94.6°
AB = 10.5 sin 94.6° / sin50.4°
AB = 13.6 km

Ship travelled 13.6 km between observations.