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Answer on Trigonometry Question for Javier Rodriguez

Question #1146

Two cars leave the same place at the same time. The first drives in a straight line N 35 Degrees W at 30 miles per hour and the second drives in a straight line N 12 Degrees E at 40 miles per hour. After 1 hour, how far apart are the cars(to the nearest mile)?

Expert's answer

The distance between the cars equals to the side of triangle with other two sides of 30 and 40 miles and the


angle between them of (35+12)= 47 degrees.
According the Law of cosines:
C2 = a2+b2 - 2 ab cos(theta)
C2 = 302+402-2*30*40*cos(47) = 863.2
C = 29.4 miles.

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