Solve right triangle with legs 5 and 12

Step-by-step solution

1. Identify the legs: $a = 5$, $b = 12$.

2. Apply Pythagorean theorem: $a^2 + b^2 = c^2$.

3. Substitute: $25 + 144 = c^2$, so $c^2 = 169$.

4. Take positive square root: $c = 13$.

5. $(5, 12, 13)$ is the second-smallest primitive Pythagorean triple (one not generated by scaling another) — appears constantly in test problems.