# 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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