SOLUTION: An airplane is flying at a velocity of 450 mph due east when it encounters a wind blowing from the southwest at 35 mph. -What is the the planes velocity relative to the ground?

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Question 453203: An airplane is flying at a velocity of 450 mph due east when it encounters a wind blowing from the southwest at 35 mph.
-What is the the planes velocity relative to the ground?
- In what direction is it flying as a result of the wind?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Due east is 090 degrees.
From the southwest is a wind from 225 degrees.
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The vector of the plane is 450 to the right.
The wind is magnitude 35 at an angle of 135 degs from the plane's vector.
The plane's ground speed = sqrt%28450%5E2+%2B+35%5E2+-+2%2A450%2A35%2Acos%28135%29%29
=~ 483.89 mph
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Use the Law of Sines to find the angle between 090 and the ground track
483.89/sin(135) = 35/sin(A)
sin(A) = 35*sin(135)/483.89
sin(A) = 0.051145
A = 2.93 degs
Heading = 090 - A = 087.07 degs
= 087 to the nearest degree