SOLUTION: Please explain how to show work for this problem and the answer: Two ships leave a port at the same time. One travels at 20 miles per hour in a direction N 32 degrees E, and t

Algebra ->  Trigonometry-basics -> SOLUTION: Please explain how to show work for this problem and the answer: Two ships leave a port at the same time. One travels at 20 miles per hour in a direction N 32 degrees E, and t      Log On


   

Question 324594: Please explain how to show work for this problem and the answer:
Two ships leave a port at the same time. One travels at 20 miles per hour in a direction N 32 degrees E, and the other travels at 28 miles per hour in a direction S 42 degrees E. How far apart are the two ships after 2 hours?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Two ships leave a port at the same time. One travels at 20 miles per hour in a direction N 32 degrees E, and the other travels at 28 miles per hour in a direction S 42 degrees E. How far apart are the two ships after 2 hours?
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One travels at 20 mph for 2 hours . = 40 miles N32 deg E
Second travels 28mph for 2 hours . = 56 miles S42 deg E
42 +32 = 74 deg angular distance
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We have to use the law of cosines to find the the distance.
distance^2= 40^2+60^2-2(40)(60)cos 74
=1600+3600*4800*cos74
=distance ^2=375.75
distance = sqrt375.75
=66.14 miles apart.