1.1.4b why third sidelength follows from the first two

If we set the lengths of legs a and b, there are infinitely many possible lengths for side c, since the length of side c changes as we vary the angle between a and b.

But if we constrain that angle to be a right angle, the situation changes: with legs a and b fixed, there is only one possible length for the hypotenuse. Because if we made c longer or shorter that would either break the triangle or destroy the right angle.

So, in a right triangle with given legs a and b, there’s exactly one possible hypotenuse length that completes leg a and leg b into a rectangular triangle—and that’s the one we find, using the Pythagorean theorem.