trig word problem, bearings
This is the problem: A ship is sailing due north. At a certain point the bearing of a lighthouse is N 38 E and the distance is 13.5. After a while, the captain notices that the bearing of the lighthouse is now S 59.4 . How far did the ship travel between the two observations of the lighthouse. distance=?
Here is what I did: at A the ship tskes a bearing of the lighthouse at C and finds angle A=38 and b=AC=13.5 miles. Later at point B, they find that angle B=59.4. So, angleC= 180-38-59.4=82.6. Next we find c, I used the law of sines, 13.5sin82.6/sin59.4= 15.6 miles.
I checked and my answer is wrong, so could someone please show me what I did wrong.