You can use the Law of Sines with ANY and ALL proofs of the Pythagorean Theorems. SIn = Opposite/hypotenuse. Law of Sines: a/sin(a) = b/sin(b) = c/sin(c) For any Right triangle: a/sin(a) = a/(a/c) = c b/sin(b) = b/(b/c) = c c/sin(c) = c/(c/c) = c For any Right triangle: a/sin(a) = b/sin(b) = c/sin(c) = c Which means for any Right Triangle: (a/sin(a))^2 = (b/sin(b))^2 = (c/sin(c))^2 = c^2 THEREFORE for any right triangle: a^2 + b^2 = (a/sin(a))^2 = (b/sin(b))^2 = (c/sin(c))^2 = c^2