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An elementary proof of the cosine law

April 12, 2011 GB High School Geometry, High School Mathematics, High School Trigonometry, Problem Solving and Proofs

The cosine law states that in triangle $ABC$ with side lengths $a, b,$ and $c$ , the following equations are satisfied:

$a ^2 = b^2 + c^2 - 2bc$ $\cos A$ *

$b ^2 = a^2 + c^2 - 2ac$ $\cos B$

$c ^2 = a^2 + b^2 - 2ab$ $\cos C$

The discussion below shows how these equations were derived. » Read more

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