The most powerful law in geometry is the Cross law, the rational analog of the Cosine law. It includes as special cases Pythagoras' theorem and the Triple quad formula. Here we sketch a purely algebraic derivation of the Cross law, and then how the other four main laws of rational trigonometry follow from it.
This video is part of the WildTrig series, which introduces Rational Trigonometry and applies it to many different aspects of geometry.
Another great job.
peterhi503 2 years ago