# How to derive the law of cosines without the pythagorean theorem

To me, it seems that the Pythagorean theorem is a special case of the law of cosines. However, all derivations that I can find seem to use the Pythagorean theorem in the derivation. Are there any simple (preferably geometric) derivations of the law of cosines that don't reference the Pythagorean theorem?

-
I think any proof of Pythagoras theorem can be adapted to get the law of cosines. –  user17762 May 21 '12 at 6:21
You might have already looked at this. But wiki has some nice collections including a proof comparing the areas of a heptagon. (en.wikipedia.org/wiki/Law_of_cosines#By_comparing_areas) –  user17762 May 21 '12 at 6:34
See my answer to "What is the most elegant proof of the Pythagorean Theorem?" : math.stackexchange.com/a/1336/409 –  Blue May 21 '12 at 6:35
Beautiful. Could you post it here so I can credit the answer? –  Nate May 21 '12 at 9:51
The law of cosines and Pythagoras theorem are equivalent. –  lhf May 21 '12 at 10:39

[As requested, posting a comment as a full answer.]

Taken from my answer to the question "What is the most elegant proof of the Pythagorean Theorem?" ...

-