The wikipedia lists a law of cosines [1] for the Bregman divergence and someone in this thread posted a proof that basically showed the law of sines follows directly from the definition of the sine. So neither form an obstruction per se, but the generalized pythagorean theorem kind of just follows directly from the definitions you need to make to even be able to say what it means for a triangle to be rectangular.

[1]: https://en.wikipedia.org/wiki/Bregman_divergence [2]: https://www.mathopenref.com/lawofsinesproof.html