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Honors Trig.

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A plane is flying at a speed and direction of 550 mph, 25 degrees north of west. There is a wind of 28 mph, at an angle of 19 degrees south of the east direction. How fast is the plane actually flying? What direction is the plane traveling?

  • Honors Trig. - ,

    Here is an easy way to do these.
    1) convert all angles to 000N,090E, 180S, 270W

    Example: 456@29deg S of E.
    = 456@119
    then convert to N, E coordinates.

    V= 456(Cos119 N + Sin119 E)

    Now for your problem:

    V= 550(cos295 N +sin295 E)+28(cos109 N+ sin109)
    combine N, E vector components:
    V= N(550cos295+28cos109)+E(550sin295+28sin109)

    do that math and you will have something like this
    V= nnnn N + eeeee E

    magnitude V= sqrt(nnnn^2+eeee^2)
    direction= arctan (eeee/nnnn)
    on the angle, be careful, as tangent is a repeating angle, it repeats each 180. So you may have to figure which quadrant.

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