1. **State the problem:** We need to find the length of the hypotenuse $h$ of a right-angled triangle with legs measuring 12.34 m and 15.2 m. 2. **Formula used:** According to the Pythagorean theorem, for a right triangle with legs $a$ and $b$ and hypotenuse $h$, the relationship is: $$h^2 = a^2 + b^2$$ 3. **Substitute the given values:** $$h^2 = 12.34^2 + 15.2^2$$ 4. **Calculate the squares:** $$h^2 = 152.2756 + 231.04$$ 5. **Add the squares:** $$h^2 = 383.3156$$ 6. **Take the square root to find $h$:** $$h = \sqrt{383.3156}$$ 7. **Calculate the square root:** $$h \approx 19.58$$ 8. **Round to one decimal place:** $$h = 19.6\text{ m}$$ **Answer:** The length of the hypotenuse is 19.6 m.