A ship is sailing due north.
At a certain point the bearing of a lighthouse is and the distance is 12.5 (miles?)
After a while, the captain notices that the bearing of the lighthouse is now .
How far did the ship travel between the two observations of the lighthouse?
| 88.5°* C
At the ship takes a bearing of the lighthouse at
. . and finds angle and miles.
Later at point , they find that angle .
. . Hence, angle
To find side , use the Law of Sines: .
So we have: .
Therefore, the distance is about miles.