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PreCalc - Vectors

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An airplane is flying with an airspeed of 660 Kilometers per hour. The wind is blowing from 345 degrees at 35 km/h. What direction should the airplane take so that, with the wind, the plane will be flying in a direction of 72 degrees?

I can compute airspeed and actual direction using law of sines and cosines but not sure how to figure out the requested 72 degree part.

  • PreCalc - Vectors -

    X = hor. = 660 + 35cos345 = km/h.

    Y = ver. = 35sin345 =

    tanA = Y/X = -9.06 / 693.8 = -.0131,
    A = -0.75 deg.

    A + B = 72,
    -0.75 + B = 72,
    B = 72 + 0.75 = 72.75 deg. = Direction.

  • PreCalc - Vectors -

    Vpw = Vp + Vw = 660[72o].
    Vp + 35[345o] = 660[72].
    Vp+35*Cos345+35*sin345=660*Cos72+660*sin72.
    Vp + 33.8-9.1i = 204+627.7i.
    Vp=204 + 627.7i -33.8+9.1i=170.2+636.8i
    = 659km/h[75o].

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