In this video I show a simple geometric proof of the cosine law. This is very useful in real world applications. Also from the proof of the cosine law you can easily proof the Pythagorean theorem as well by setting the angle equal to 90 degrees.

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Trigonometry Proofs: Law of Cosines

Geometric Proof of the Cosine Law

Corollary: Proof of the Pythagorean Theorem

Example