1. **State the problem:** We have a right triangle with two legs given: one leg is 3 units and the other leg is 7 units. We need to find the length of the hypotenuse (the side opposite the right angle). 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$c = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are the legs, and $c$ is the hypotenuse. 3. **Apply the formula:** Substitute $a=3$ and $b=7$: $$c = \sqrt{3^2 + 7^2} = \sqrt{9 + 49} = \sqrt{58}$$ 4. **Calculate the square root:** $$c \approx 7.6157$$ 5. **Round to the nearest thousandth:** $$c \approx 7.616$$ **Final answer:** The length of the hypotenuse is approximately **7.616** units.