posted by John .
An airplane is headed on a bearing of 140° with an air speed of 500 miles per hour. The course has a bearing of 128°. The ground speed is 580 miles per hour. Find the drift angle, the wind direction, and the wind speed.
drift angle is clearly 12°
Make a sketch to have a triangle with sides 500 and 580 with 12° as the contained angle.
Using cosine law, let the third side be R (the wind speed)
R^2 = 500^2 + 580^2 - 2(500(580)cos12°
R = ....
then use the Sine Law to find one of the other angles , etc
580[128o] + Vw = 500[140o].
580*sin128+i580*Cos128 + Vw = 500*sin140+i500*Cos140.
457-357.1i + Vw = 321.4-383i,
Vw = 321.4-457-383i+357.1i = -135.6 - 25.9i = 138mi/h[79.2o]Cw from +Y-axis. = Velocity of the wind.
NOTE: For clockwise rotation from +Y-axis(Bearing), the X-component is found by multiplying by the sine of the angle.
Multiply by the cosine to fine the Y-component.
Tan A = X/Y instead of Y/X.