1. **State the problem:** We have a right triangle with legs of lengths 18 m and 24 m, and we want 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:** Here, $a = 18$ m and $b = 24$ m, so: $$c^2 = 18^2 + 24^2$$ 4. **Calculate squares:** $$c^2 = 324 + 576$$ 5. **Sum the squares:** $$c^2 = 900$$ 6. **Find $c$ by taking the square root:** $$c = \sqrt{900}$$ 7. **Simplify the square root:** $$c = 30$$ 8. **Conclusion:** The length of the hypotenuse $c$ is 30 meters. Final answer: $c = 30$ meters.