Math- Please Help!!

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An airplane has an airspeed of 724 kilometers per hour at a bearing of 30 degrees.The wind velocity is 32 kilometers per hour from the west. What are the groundspeed and the direction of the plane?

  • Math- Please Help!! -

    739 kilometers per hour. I used an online electronic flight computer.

  • Math- Please Help!! -

    make a diagram.
    from the origin draw a vector with a bearing of 30 degrees and mark its length 724. Call it OA
    Draw a horizontal line AB of length 32
    the angle OAB = 120 degrees

    by cosine law:
    OB^2 = 724^2+32^2-2(724)(32)cos120
    = 548368
    OB= 740.5

    now by the Sine Law:
    sinO/32 = sin120/740.5
    sinO= .0374235
    angleO=2.145
    so the bearing is 30+2.1 or 31.1 degrees, and the ground speed is 740.5 km/h

    check my arithmetic

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