SOLUTION: To fly due north at 580km/h when there is a 45km/h wind blowing from 130degrees, with what heading and speed should a plane travel? Thanks so much!

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Question 310051: To fly due north at 580km/h when there is a 45km/h wind blowing from 130degrees, with what heading and speed should a plane travel?
Thanks so much!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
To fly due north at 580km/h when there is a 45km/h wind blowing from 130degrees, with what heading and speed should a plane travel?
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North is a direction of 360º or 0º.
A wind from 130º makes a 50º interior from north (180-130).
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The plane's airspeed is
= sqrt%28b%5E2+%2B+c%5E2+-+2bc%2Acos%2850%29%29
= sqrt%28580%5E2+%2B+45%5E2+-+2%2A580%2A45%2Acos%2850%29%29
= 567.14 kph
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The heading:
sin(B)/45 = sin(50)/567.14
sin(B) = 0.060782
B = 3.48º
Heading = 3.48º