How do you know on a right triangle which leg is a or b (pythagorean theorem)

The real answer is: it doesn’t matter! a and b are just labels we give to the legs; it doesn’t matter how you pick them, especially since addition is *commutative* (order doesn’t matter). An equality valid way of writing the equation would be:

(leg 1)^2 + (leg 2)^2 = (hypotenuse)^2

But it saves time to just write it as a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse.