Hello, qbkr21!

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? Code:

B *
| *
| *
|42.9°*
| *
c| *
| 88.5°* C
| *
|48.6°* b=12.5
| *
A *

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.