Trigonometry

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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.

  • Trigonometry -

    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

  • Trigonometry -

    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.

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