Question

from a ship two lighthouses bear north 40 degree east. after the ship sails at 15knots on a course of 135 degrees for 1 hr, 20 min, the lighthouses bear 10 degrees and 345 degrees. find the distance of the ship in the latter position to the farther lighthouse.

Answer 1

Looks like Steve answered the same question in the first of the "Related Questions" below

http://www.jiskha.com/display.cgi?id=1410269873

Answer 2

This one takes some drawing. Let's label the near lighthouse A, and the far one B.
The ship began at P, and ended up at Q.

It helps to draw a line due north from Q. A bit of analysis shows that
PQ = 20 mi
∠BPQ = 95°
∠PBQ = 30°

We want the distance QB, from the later ship's position to lighthouse B.

Using the law of sines,
20/sin30° = BQ/sin95°
BQ = 39.85 naut. mi.

Answer 3

Looks like I used some different angles last time. I hope both methods produce the same answer!!