proof of cosines law

Let a, b, c be the sides of a triangle and α, β, γ its angles, respectively.  By the projection formula, one may write the equalities


Multiplying the equalities by a, -b and -c, respectively, they read


Addition of these yields the sum equation




which is the cosines law.

Title proof of cosines law
Canonical name ProofOfCosinesLaw
Date of creation 2013-03-22 18:27:13
Last modified on 2013-03-22 18:27:13
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 4
Author pahio (2872)
Entry type Proof
Classification msc 51M04
Related topic DerivationOfCosinesLaw