Proof of the Law of Cosines

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High School Math based on the topics required for the Regents Exam conducted by NYSED.

What is the Law of Cosines?
We can use the Law of Cosines to find the length of a side or size of an angle.
For a triangle with sides a,b and c and angles A, B and C the Law of Cosines can be written as:
To find side:
\[a^2 = b^2 + c^2 - 2bc Cos A\]
We can rearrange the above formula to find angle:
\[\cos A = \frac{{{b^2} + {c^2} - {a^2}}}{{2bc}}\]

How to derive the Law of Cosines?

Trigonometry - Derivation of Law Cosines The derivation of the Law of Cosines and then a couple of examples using it. Mathematical Proofs:
The Cosine Rule A step by step guide as to how the Cosine rule was derived. Law of cosines