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Law of sines or cosines: Two cars leave the city at the same time and travel along straight roads that leave the city at
an angle of 80 degree angle. One car is traveling at a rate of 60 mph and the other at a rate of 70 mph.
How far apart will the cars be after 1 hour and 30 minutes?
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Law of cosines. See the lesson Proof of the Law of Cosines revisited in this site.
One side of the triangle is 60 mph * 1.5 hours = 90 miles.
The other side is 70 mph * 1.5 hours = 105 miles.
The angle between these sides is 80°.
Hence, the third side is
= 125.87 miles.
It is the distance between the cars after 1 hour and 30 minutes.