The Law of Cosines

Question

You are on a fishing boat that leaves it's pier and heads east. After traveling for 25 miles, there is a report warning of rough seas directly south. The captain turns the boat and follows a bearing of S 40 degrees W for 13.1 miles.

A. At this time. how far are you from the boat's pier?

B. What bearing could the boat have originally taken to arrive at this spot?

Answer 1

As to the heading needed sailing from the dock,

sin θ / 13.1 = sin 50º / 19.38

θ shall be S of E.

Answer 2

A)

Use the law of cosines with a = 25, b = 13.1, and the measure of angle C as 50 degrees (90 - 40 = 50):

You should get 19.38 miles.

B)

It is not clear how you would go 25 miles in any direction and be able to return to your original location in just 13.1 miles. Can you check to see if the problem wording given is correct?