1. **State the problem:** We need to find the length of the unknown leg of a right triangle where one leg is 12.75 and the hypotenuse is 37.25. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$c^2 = a^2 + b^2$$ where $c$ is the hypotenuse, and $a$, $b$ are the legs. 3. **Identify known values:** - Hypotenuse $c = 37.25$ - One leg $a = 12.75$ - Unknown leg $b = ?$ 4. **Apply the formula:** $$b^2 = c^2 - a^2$$ 5. **Calculate squares:** $$b^2 = 37.25^2 - 12.75^2$$ $$b^2 = 1387.5625 - 162.5625$$ 6. **Subtract:** $$b^2 = 1225$$ 7. **Find $b$ by taking the square root:** $$b = \sqrt{1225}$$ 8. **Simplify the square root:** $$b = 35$$ **Final answer:** The length of the unknown leg is $35$.