A ship sailing west toward shore, and there are tow ports on the horizon. The ports are 17 miles apart, and from the ship's vantage point, point A is 30 deg North of straight ahead and port B is 80 deg South of straight ahead. Approximately how much farther is it fro the ship to dock at port B than at Port A?

Answer 1

using the law of sines, if A is x miles away, and B is y miles away,

x/sin10° = y/sin60° = 17/sin110°

Now you can find x and y, and thus y-x.