SOLUTION: A plane flies 500 kilometers with a bearing of N 44 degrees W from B to C. The plane then flies 720 KM from C to A. Find the bearing of the flight from C to A. Here is a picture o

Algebra ->  Trigonometry-basics -> SOLUTION: A plane flies 500 kilometers with a bearing of N 44 degrees W from B to C. The plane then flies 720 KM from C to A. Find the bearing of the flight from C to A. Here is a picture o      Log On


   

Question 388061: A plane flies 500 kilometers with a bearing of N 44 degrees W from B to C. The plane then flies 720 KM from C to A. Find the bearing of the flight from C to A.
Here is a picture of the diagram
http://i763.photobucket.com/albums/xx275/trinhkieu888/9-1.jpg

thanks for the help!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Convert both displacements to x,y coordinates.
Positive x is East.
Positive y is North.
Angle is measured CCW from x-axis.
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D%5BBC%5D=(500%2Acos%2890%2B44%29,500%2Asin%2890%2B44%29)
D%5BCA%5D=(720%2Acos%28180%2Bbeta%29,720%2Asin%28180%2Bbeta%29)
where
720%2Asin%28beta%29=500%2Asin%2846%29
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720%2Asin%28beta%29=500%2Asin%2846%29
sin%28beta%29=%28500%2F720%29%2Asin%2846%29
sin%28beta%29=0.4995
beta=30
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D%5BBC%5D=(500%2Acos%28134%29,500%2Asin%28134%29)
D%5BBC%5D=(-347.3,359.7)
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D%5BCA%5D=(720%2Acos%28210%29,720%2Asin%28210%29)
D%5BCA%5D=(-623.5,-360)
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D=D%5BBC%5D%2BD%5BCA%5D
D=(-347-623,360-360)
D=(-970,0)
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The plane is 970 km from the starting point due west.