Law of Cosines
In class we were talking about relating the Law of Cosines to the Pythagorean Theorem. Most of the proofs I know for the one come from the other.
So here's a look at the LoC from the viewpoint of Euclid's slick proof of the Pythagorean Theorem, and using the favorite Greek geometry trick, dropping an altitude.
Irina Boyadzhiev has a sweet animation of the proof from this viewpoint. https://www.geogebratube.org/student/m105989