1. **Stating the problem:** We have a right triangle with one leg labeled $b$, the other leg labeled $a$, and the hypotenuse labeled $c=6$. We want to find the values of $a$ and $b$ or solve for the triangle's sides given $c=6$ and the right angle. 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. **Applying the formula:** Given $c=6$, we have: $$6^2 = a^2 + b^2$$ which simplifies to: $$36 = a^2 + b^2$$ 4. **Explanation:** This equation means the sum of the squares of the legs equals 36. Without additional information about $a$ or $b$, we cannot find unique values but can express one leg in terms of the other. 5. **Expressing $b$ in terms of $a$:** $$b^2 = 36 - a^2$$ $$b = \sqrt{36 - a^2}$$ 6. **Summary:** The legs $a$ and $b$ satisfy $a^2 + b^2 = 36$. For any $a$ between 0 and 6, $b$ is given by $b = \sqrt{36 - a^2}$. This completes the solution for the right triangle with hypotenuse 6.