math

A triangle has a 13-inch side, a 14-inch side, and a 15-inch side. To the nearest tenth
of an inch, how long is the median drawn to the 14-inch side?

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  1. I just got the answer 14 is that right? I formed a parallelogram and added the vector lengths and multiplied it by 1/2.

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  2. Nope. You have ignored the triangle inequality.

    From the law of cosines, the angle ? between the 13 and 15 sides is

    14^2 = 13^2+15^2-2*13*15 cos?
    ? = 59.5°

    So, if we let the short side be

    u = 13i

    The 15" side is

    v = 7.62i + 12.92j

    The median m is then

    m = (u+v)/2 = (20.62i + 12.92j)/2
    = 10.31i + 6.47j
    |m| = 12.17

    Or, use the handy formula found here:

    http://www.cut-the-knot.org/triangle/LengthOfMedian.shtml

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