Question

Two ships leave a port at 9 A.M. One travels
at a bearing of N 53
◦ W at 12 miles per hour
and the other travels at a bearing of S 67
◦ W
at 16 miles per hour.
Approximate how far apart they are at
noon that day.
Answer in units of mi

Answer 1

After you draw your picture, you see that you are talking about a triangle with a 60 degree angle. The sides that form the 60 degree angle are 3(12) and 3(16) or 36 and 48. So now you can use the law of cosines using the 60 degree angle as C and the required distance as c. So: c^2 = 48^2+36^2 - 2(48)(36)cos 60
c^2 = 2304+1296-3456(.5)
c^2 = 3600-1728
c^2 = 1872
c = 43.3 miles