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Given 2 sides, and an angle between those two sides, what is the simplest proof you can come up with to find the measure of the 3rd side?

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    http://www.proofwiki.org/wiki/Law_of_Cosines2012-04-25
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    Wikipedia (http://en.wikipedia.org/wiki/Law_of_cosines) offers several different proofs.2012-04-25
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    I like the one using the Pythagorean theorem because it shows that the law of cosines is *equivalent* to the Pythagorean theorem.2012-04-25
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    I think the ordering by elegance and the ordering by simplicity are partial orders, not total orders. I'm sure there are plenty of maximal elements in the corresponding set, but I'm not sure there is a maximum (even if each of the orders is total, the product order is not...) (-;2012-04-25

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