SOLUTION: A plane's air speed is 270 km/h, and its heading is 70degrees. Find its ground speed and true-course bearing if a wind of 50 km/h is blowing from due north. Please help. Thank

Question 310114: A plane's air speed is 270 km/h, and its heading is 70degrees. Find its ground speed and true-course bearing if a wind of 50 km/h is blowing from due north.
Please help.
Thank You so much!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Sketch a triangle with one side 270 at an angle of 70� to the right of vertical (the plane's speed vector).
At the end, draw a line 50 units long at an angle of 180 (from north), a vertical down from the end of the plane's vector. This vertex is angle B
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This makes a triangle with the interior angle B of 70�.
The 3rd side is the ground speed.
Use the Cosine Law:
b^2 = a^2 + c^2 - 2*a*c*cos(70)
b^2 = 270^2 + 50^2 - 2*270*50*cos(70)
b^2 =~ 66165.456
b =~ 257.23 kph
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I suppose a "true course bearing" is the ground track.
Use the Law of Sines to find angle A.
sin(A)/50 = sin(70)/b
sin(A) = 50*sin(70)/257.23
sin(A) =~ 0.1826586
A =~ 10.525�
Ground track = A + 70
= 80.5�

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