1. **State the problem:** We have a right triangle with legs of lengths 8 and 6, and we want to find the length of the hypotenuse $a$. 2. **Formula used:** In a right triangle, the Pythagorean theorem states: $$a^2 = b^2 + c^2$$ where $a$ is the hypotenuse, and $b$ and $c$ are the legs. 3. **Apply the formula:** Here, $b=8$ and $c=6$, so: $$a^2 = 8^2 + 6^2$$ 4. **Calculate squares:** $$a^2 = 64 + 36$$ 5. **Sum the squares:** $$a^2 = 100$$ 6. **Find $a$ by taking the square root:** $$a = \sqrt{100}$$ 7. **Simplify the square root:** $$a = 10$$ **Answer:** The length of the hypotenuse $a$ is 10.