A Conversation for Triangles
Expaning Pythagoras
Apollyon - Grammar Fascist Started conversation Feb 22, 2006
As it turns out, Pythagors' Theorem is a special case of this:
Let A, B, and C be three angles of a triangle, and a, b, and c be the three respective opposite sides (ie A is opposite a, B is opposite b, and C is opposite c.)
a^2 = b^2 + c^2 - 2bc(cosA)
b^2 = a^2 + c^2 - 2ac(cosB)
c^2 = a^2 + b^2 - 2ab(cosC)
When the angle in question is a right angle, its cosine is 0, and so the above equations reduce to Pythagoras.
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Expaning Pythagoras
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