1. The problem states we have a right triangle with hypotenuse 10, one side 8, and the other side $x$. We need to find $x$. 2. According to the Pythagorean theorem, in a right triangle $a^2 + b^2 = c^2$ where $c$ is the hypotenuse. 3. Here, let $a=8$, $b=x$, and $c=10$. 4. Substitute the known values: $$8^2 + x^2 = 10^2$$ 5. Calculate the squares: $$64 + x^2 = 100$$ 6. Subtract 64 from both sides: $$x^2 = 100 - 64 = 36$$ 7. Take the square root of both sides: $$x = \sqrt{36} = 6$$ 8. The value of $x$ is 6.