1. **State the problem:** We have a right triangle with legs of lengths 60 meters and 80 meters, 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 $a = 60$ and $b = 80$: $$c^2 = 60^2 + 80^2$$ 4. **Calculate squares:** $$c^2 = 3600 + 6400$$ 5. **Sum the squares:** $$c^2 = 10000$$ 6. **Find $c$ by taking the square root:** $$c = \sqrt{10000}$$ 7. **Simplify the square root:** $$c = 100$$ 8. **Final answer:** The length of the hypotenuse is $100$ meters.