Two ships leave the same port at the same time. One ship sails on a course of 110 degree at 32 mi/h. The other sails on a course of 230 degree at 40 mi/h. Find the distance between them after 2 hours. Express your answer to the nearest mile.

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  1. both start at origin
    Ship one
    110 from north is 20 degrees below +x axis
    x1 = 2 * 32 * cos 20
    y1 = -2 * 32 * sin 20
    Ship 2
    230 from north is 40 deg below -x axis
    x2 = -2 * 40 cos 40
    y2 = -2 * 40 sin 40

    d = sqrt [(x2-x1)^2 + (y2-y1)^2 ]

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  2. or, since the angle between their travel is 120° use the law of cosines to find the 3rd side of the triangle:

    d^2 = 64^2 + 80^2 - 2*64*80 cos 120°

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