SOLUTION: a car leaves an intersection traveling at an average speed of 56 miles per hour. ten minutes later a second car leave the same intersection and travels on a road making an angle of

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Question 1062292: a car leaves an intersection traveling at an average speed of 56 miles per hour. ten minutes later a second car leave the same intersection and travels on a road making an angle of 112 with the first car, at an average speed of 54 miles per house. assuming the roads are straight, how far apart are the cars 30 minutes after the first car has left?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
                      SPEED          TIME       DISTANCE

FIRSTCAR               56           t          56t%29
SECCAR                 54            t%2B1%2F6     54%2A%28t%2B1%2F6%29
DISTANCE 112 Degrees                            Law Of Cosines


Careful with Law of Cosines. The angle between the cars is 112 degrees and the cosine must be the negative value. -cos%28112-90%29=-cos%2822%29=-0.92718=cos%28112%29

Distance d between the cars any time t is



That is the formula. Simplify any way you like, and then substitute t=1%2F2 to evaluate d.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
a car leaves an intersection traveling at an average speed of 56 miles per hour.
ten minutes later a second car leave the same intersection and travels on a road making an angle of 112 with the first car,
at an average speed of 54 miles per house. assuming the roads are straight, how far apart are the cars
30 minutes after the first car has left?
~~~~~~~~~~~~~~~~~~~~~~~~ 

30 minutes after the first car has left, it was 56%2A%281%2F2%29 = 28 miles from the intersection.

30 minutes after the first car has left, the second car was %281%2F3%29%2A54 = 18 miles from the intersection.

The distance under the question is 

sqrt%2828%5E2+%2B+18%5E2+-+28%2A18%2Acos%28112%5Eo%29%29 = calculate.

Writing by "josgarithmetic" is not the way solving this problem.