SOLUTION: Please help me. Two cars leave from the same spot at the same time, traveling on straight roads that intersect at an angle of 63 degrees. One car is traveling at 45 mph, and the

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me. Two cars leave from the same spot at the same time, traveling on straight roads that intersect at an angle of 63 degrees. One car is traveling at 45 mph, and the      Log On


   

Question 385633: Please help me.
Two cars leave from the same spot at the same time, traveling on straight roads that intersect at an angle of 63 degrees. One car is traveling at 45 mph, and the other at 50 mph. After 3 hours what is the distance between the cars? In the solution, I have to show a diagram of the problem.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two cars leave from the same spot at the same time, traveling on straight roads
that intersect at an angle of 63 degrees.
One car is traveling at 45 mph, and the other at 50 mph.
After 3 hours what is the distance between the cars?
:
Find the distance each car traveled in 3 hrs
Car 1: 3(45) = 135 mi
Car 2: 3(50) = 150 mi
:
A diagram would be helpful
:
Draw a triangle Angles: A, B, C
A = 63 degrees, side opposite is side a, which is the distance between the cars after 3 hrs.
Side b = 150
side c = 120
:
The law of cosines will work nicely here: a^2 = b^2 + c^2 -(2*a*b*cos(A)
:
Find the cosine of 63: .45399
Enter into your calc to find a
sqrt%28%28150%5E2%2B135%5E2%29+-+%282%28150%2A135%29%2A.45399%29%29
a = 149.46 mi between them in 3 hrs