1. **State the problem:** We have a right triangle with legs of lengths 12 feet and 5 feet, and we need to find the length of the hypotenuse $c$. 2. **Formula used:** According to the Pythagorean theorem, for a right triangle with legs $a$ and $b$ and hypotenuse $c$, the relationship is: $$c^2 = a^2 + b^2$$ 3. **Apply the formula:** Substitute $a = 12$ and $b = 5$: $$c^2 = 12^2 + 5^2$$ $$c^2 = 144 + 25$$ $$c^2 = 169$$ 4. **Solve for $c$:** Take the square root of both sides: $$c = \sqrt{169}$$ 5. **Simplify:** $$c = 13$$ 6. **Answer:** The length of the hypotenuse $c$ is 13 feet. This is exact, so no rounding is necessary.