Question 1067707: A plane flies from Colorado Springs due north to Denver, a distance of 70 miles. Due to bad weather, the plane cannot fly directly to Denver, instead the plane takes off at a bearing of N 60˚W. After flying 57 miles, the plane turns and flies directly toward Denver. After turning directly back toward Denver, how far does the plane have to travel to get to Denver?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A plane flies from Colorado Springs due north to Denver, a distance of 70 miles.
Due to bad weather, the plane cannot fly directly to Denver, instead the plane takes off at a bearing of N 60˚W.
After flying 57 miles, the plane turns and flies directly toward Denver.
After turning directly back toward Denver, how far does the plane have to travel to get to Denver?
:
Draw a triangle ABC to represent this where:
ColoSpr is at C, Denver is at B, Turning point is at A
and
C = 60 degrees
a = 70 mi
b = 57 mi
c = distance to Denver
Use the law of cosines to find c
c^2 = a^2 + b^2 - 2(ab)*cos(C)
c^2 = 70^2 + 57^2 - 2(70*57)*cos(60)
c^2 = 4900 + 3249 - 2(70*57)*.5
c^2 = 8149 - 3990
c = 
c = 64.49 mi
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