Trig

A plane is flying at 240 mph heading North 60 degrees East. The wind is blowing at South 30 degrees East at 30 mph.

What is the largest and smallest angles?

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  1. Vp = 240mi/h, N60E = 30deg CCW.

    Vw = 30mi/h, S30E = 300deg. CCW.

    Add all hor components of velocity; and
    then add all ver. components.

    X = hor = 240cos30 + 30cos300 =
    207.8 + 15 = 222.8mi/h.

    Y = ver = 240sin30 + 30sin300 =
    120 - 26 = 94mi/h.

    Now we have a single rt triangle with
    X and Y representing the hor and ver
    side, respectively.

    tanA = Y/X = 94/222.8 = 0.4219,
    A = 22.9deg.,CCW = N67.1E. = Bearing of
    the plane.

    The largest angle = 90deg.

    The smallest angle = 22.9deg.,CCW.

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