1. **State the problem:** We have a right triangle with one leg of length 6 and the hypotenuse of length 10. We need to find the length of the other leg. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse, and $a$ and $b$ are the legs. 3. **Assign values:** Let the unknown leg be $x$. Then: $$6^2 + x^2 = 10^2$$ 4. **Calculate squares:** $$36 + x^2 = 100$$ 5. **Isolate $x^2$:** $$x^2 = 100 - 36$$ $$x^2 = 64$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{64}$$ 7. **Simplify the square root:** $$x = 8$$ **Final answer:** The length of the third side is $8$.