SOLUTION: Two cargo boats leave the same port at the same time. The direction of one boat is at an angle of 30 degrees to the other. If the ratio of the speed of the first boat to the second

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Question 1125558: Two cargo boats leave the same port at the same time. The direction of one boat is at an angle of 30 degrees to the other. If the ratio of the speed of the first boat to the second boat is √3/2, and if the second boat travels at 18 km/h, how far apart, in km, are they at the end of 5 hours.
A)45
B)90
C)60
D)45√3
E)30
Answer by MathLover1(20849) About Me  (Show Source):
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Find the speed of the 1st boat (s)
s%2F18 = sqrt%283%29%2F2....cross multiply
2s+=+18%2Asqrt%283%29
s+=+31.177%2F2
s+=+15.6+%28km%2Fh%29 is the speed of the 2nd boat

Find the distance each has traveled in 5 hrs
5%2A15.6+=+78km traveled by the 1st boat
5%2A18+=+90km by the 2nd boat

The distance between the boat is the side (a) opposite the 30 degree angle (A)
Use the law of cosines:
a%5E2+=+b%5E2+%2B+c%5E2+-+2bc%2ACos%28a%29,where
b+=+78
c+=+90
a%5E2+=+78%5E2+%2B+90%5E2+-+2%2878%2A90%29%2ACos%2830%29
a%5E2+=+6084+%2B+8100+-+2%287020%29%2A.866
Do the math
a+=+sqrt%282025%29
a+=+45km apart in 5 hrs

so, answer is A)45