SOLUTION: 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

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Question 1013987: 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 60mph and the other at a rate of 70 mphmph. How far apart will the cars be after 1 hour and 30m30minutes?
Answer by ikleyn(52855) About Me  (Show Source):
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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 

sqrt%2890%5E2+%2B+105%5E2+-+2%2A90%2A105%2Acos%2880%5Eo%29%29 = 125.87 miles.

It is the distance between the cars after 1 hour and 30 minutes.