SOLUTION: Two ships leave a harbor at the same time, traveling on courses that have an angle of 120 ^\circ between them. If the first ship travels at 20 miles per hour and the second ship tr

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Question 803232: Two ships leave a harbor at the same time, traveling on courses that have an angle of 120 ^\circ between them. If the first ship travels at 20 miles per hour and the second ship travels at 37 miles per hour, how far apart are the two ships after 1.7 hours?

Answer by ankor@dixie-net.com(22740) (Show Source):
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Two ships leave a harbor at the same time, traveling on courses that have an angle of 120 ^\circ between them.
If the first ship travels at 20 miles per hour and the second ship travels at 37 miles per hour, how far apart are the two ships after 1.7 hours?
:
Find how far each ship has traveled in 1.7 hrs
First: 1.7 * 20 = 34 miles
2nd: 1.7 * 37 ~ 63 miles
:
Use the law of cosines a^2 = b^2 + c^2 - 2(bc)*cos(A); where
a = distance between the ships after 1.7 hrs
A = 120 degrees
b = 34 mi
c = 63 mi
:
a^2 = 34^2 + 63^2 - 2(34*63)*cos(120)
a^2 = 1156 + 3969 - 2(2142)*-.5
a^2 = 5125 - (-2142)
a^2 = 5125 + 2142
a =
a ~ 85 miles apart in 1.7 hrs