1. **Stating the problem:** We have a right triangle with one leg measuring 112 m, and we want to find the length of the hypotenuse or the other leg based on the given options. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$c^2 = a^2 + b^2$$ where $c$ is the hypotenuse, and $a$ and $b$ are the legs. 3. **Important rule:** The hypotenuse is always the longest side opposite the right angle. 4. **Given:** One leg $a = 112$ m. We need to check which of the options could be the hypotenuse or the other leg. 5. **Check each option:** - Option a) 32.86 m is less than 112 m, so it cannot be the hypotenuse. - Option b) 52.20 m is less than 112 m, so it cannot be the hypotenuse. - Option c) 63.03 m is less than 112 m, so it cannot be the hypotenuse. - Option d) 74.94 m is less than 112 m, so it cannot be the hypotenuse. 6. **Conclusion:** Since all options are less than 112 m, none can be the hypotenuse if 112 m is a leg. Possibly, the 112 m is the hypotenuse, and the options are legs. 7. **Calculate the other leg $b$ using the Pythagorean theorem:** $$b = \sqrt{c^2 - a^2}$$ Assuming $c = 112$ m and $a$ is one of the options, calculate $b$ for each: - For $a = 32.86$ m: $$b = \sqrt{112^2 - 32.86^2} = \sqrt{12544 - 1079.4} = \sqrt{11464.6} \approx 107.1\,m$$ - For $a = 52.20$ m: $$b = \sqrt{112^2 - 52.20^2} = \sqrt{12544 - 2724.8} = \sqrt{9819.2} \approx 99.1\,m$$ - For $a = 63.03$ m: $$b = \sqrt{112^2 - 63.03^2} = \sqrt{12544 - 3973.8} = \sqrt{8570.2} \approx 92.6\,m$$ - For $a = 74.94$ m: $$b = \sqrt{112^2 - 74.94^2} = \sqrt{12544 - 5616.0} = \sqrt{6928.0} \approx 83.2\,m$$ Since the problem does not specify which side to find, these are the possible other legs corresponding to each option. **Final answer:** The options given are possible leg lengths, and the other leg can be calculated as above.