1. **State the problem:** A carpenter claims that in a 30°-60°-90° triangle with hypotenuse 12 m, the other two sides must be 6 m and 10.39 m. 2. **Recall the properties of a 30°-60°-90° triangle:** The sides are in the ratio $1 : \sqrt{3} : 2$, where the shortest side (opposite 30°) is half the hypotenuse, and the longer leg (opposite 60°) is $\frac{\sqrt{3}}{2}$ times the hypotenuse. 3. **Calculate the sides based on the hypotenuse:** - Shortest side $= \frac{1}{2} \times 12 = 6$ - Longer leg $= \frac{\sqrt{3}}{2} \times 12 = 6\sqrt{3} \approx 10.39$ 4. **Evaluate the carpenter's claim:** - The shortest side is correctly 6 m. - The longer leg is approximately 10.39 m, which matches the carpenter's claim. 5. **Check the sum of the legs compared to the hypotenuse:** The sum $6 + 10.39 = 16.39$ which is not equal to the hypotenuse 12, but this is not a requirement for right triangles. 6. **Check if the triangle is isosceles:** A 30°-60°-90° triangle is not isosceles; the legs are different lengths. 7. **Conclusion:** The carpenter's claim is correct based on the special triangle theorem. **Final answer:** Statement A is correct.