A Conversation for Triangles

Expaning Pythagoras

Post 1

Apollyon - Grammar Fascist

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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