[version_five]

I once read a book that proposed a "new" trigonometry that iirc worked with the hypotenuse squared and maybe the sin^2 of an angle as it's base quantities, and the author showed how easy it was to do stuff. This feels about the same. Not wrong, but not really useful once you've learned the usual way to do it, not easier to learn, and you'll be forever confused if it's all you learn.

[kevin_thibedeau]

Trigonometry is really about circles and rotations. The triangles are just an artifact of static diagramming. Zeroing in on triangle properties suggests a lack of fundamental understanding.