SOLUTION: Two straight roads diverge at an angle of 75�. Two cars leave the intersection at 2:00 P.M., one traveling at 56 mi/h and the other at 36 mi/h. How far apart are the cars at 2:30 P

Question 1030224: Two straight roads diverge at an angle of 75�. Two cars leave the intersection at 2:00 P.M., one traveling at 56 mi/h and the other at 36 mi/h. How far apart are the cars at 2:30 P.M.? (Round your answer to two decimal places.)
Answer: mi
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
Your problem is best explained
as a triangle ABC
The two roads diverging at
an angle of 75 degrees are
AB and AC.
The angle at A is 75 degrees
AB = car travelling at 56 mi/hr
after half an hour AB = 28 miles
AC = car travelling at 36 mi/hr
after half an hour AC = 18 miles
Using Cosine rule.
BC^2 = AB^2 + AC^2 - 2 x AB x AC x Cos(75)
BC^2 = 28^2 + 18^2 - (2 x 28 x 18 x Cos(75))
BC = √847.11
BC = 29.11 miles (2 decimal places)
Cars are 29.11 miles apart.
Hope this helps :-)
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