>> Does this qualify as yet another proof, or too close to proof 6?
>
>Do not know what other could say. Far as I am concerned, for
>this proof you do not even need trigonomentry. IMHO, the use
>of sine and cosine is entirely accidental and redundant.

How true. One does not need to restate the obvious. I suppose this is only a highlight of the fact that the PT is a generalization of the Cosine Law.