$a^2 + b^2 = c^2$ (read aloud: a-squared plus b-squared equals c-squared). The two shorter sides (the legs, $a$ and $b$) have squares that together exactly fill the square on the hypotenuse $c$. It has worked for every right triangle for two and a half thousand years, and it asks for no angles at all — two sides in, the third side out.

The one decision is direction. Hunting the hypotenuse? ADD the squares: $c = \sqrt{a^2 + b^2}$. Hunting a leg? SUBTRACT: $a = \sqrt{c^2 - b^2}$ — a leg must come out shorter than $c$, and subtracting is what keeps it honest. And meet the 3-4-5 family: $9 + 16 = 25$, and it works scaled by anything — 6-8-10, 9-12-15. Exams adore it; from today you’ll recognize it on sight.