Question 1177806: Two ships leave a harbor at the same time, traveling on courses that have an angle of 140∘ between them. If the first ship travels at 24 miles per hour and the second ship travels at 40 miles per hour, how far apart are the two ships after 2.8 hours?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! If you draw this as the start is O, and ship 1 is A and ship 2 B, the distance apart is o. The two legs of the obtuse triangle are 67.2 miles and 112 miles. Use the Law of Cosines:
o^2=a^2+b^2-2ab cos O
=67.2^2+112^2-2(67.2*112)cos 140
=28590.95 miles^2
o=169.09 miles apart, which is the answer. If they had gone in opposite directions, they would have been 179.2 miles apart.
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by the law of sines, angle A is 25.2 degrees and angle B is 14.8 degrees
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