Question 1022497
A plane is flying 215 miles per hour toward the Southeast (Theta Angle is 315 degrees).  A wind suddenly blows at 75 miles per hour from the North to the South (Theta Angle is 270 degrees).  Remember you will have to find the X-components & Y-components of the plane and wind.

New velocity of plane

Angle Alpha is 

Angle Theta is
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In aviation (and other navigation) North is 0/360 degs, and angles are measured clockwise.
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The plane's heading is 135 degs.
The wind is 360 @ 75.
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Draw a triangle with a leg of length 215 (the speed) at 135 degs.
From the lower right end, draw a vertical line of length 75 (windspeed).
The angle between the 2 legs is 135 degs.
Use the Cosine Law to find the 3rd side (the resultant ground speed).
{{{c^2 = a^2 + b^2 - 2ab*cos(135)}}}
{{{c^2 = 215^2 + 75^2 - 2*215*75*(-sqrt(2)/2)}}}
{{{c^2 = 74654.194}}}
c =~ 273.23 mi/hr (the groundspeed)
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Call the angle between the plane's heading and its ground track A:
Use the Sine Law:
sin(A)/75 = sin(135)/273.23
sin(A) =~ 0.194
A = 11.19 degs
--> ground track = 146.19 degs
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Angle on the x-y plane = 303.8 degs

The ground track = 135 + angle A
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It's not clear what angles alpha and theta are located.
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PS  Pilots don't do trig, they use computers of various types to do it for them.