Explain the connection between pythagorean triples and right triangles. and

The Pythagorean triples are integer solutions to the Pythagorean theorem
a*a + b*b = c*c or    x squared + y squared = z squared you can use abc and xyz interchangeably. using a right triangle, the c side would be the hypotenuse, the side opposite the right angle. The "a" side is the shorter of the two sides adjacent to the right angle.