1. **State the problem:** We have a right triangle with one leg measuring 8 cm, the hypotenuse measuring 10 cm, and the other leg labeled as $x$. We need to find the length of $x$ rounded to the nearest tenth. 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. **Apply the formula:** Let the legs be $8$ cm and $x$ cm, and the hypotenuse be $10$ cm. $$8^2 + x^2 = 10^2$$ 4. **Calculate squares:** $$64 + x^2 = 100$$ 5. **Isolate $x^2$:** $$x^2 = 100 - 64$$ $$x^2 = 36$$ 6. **Take the square root:** $$x = \sqrt{36}$$ $$x = 6$$ 7. **Answer:** The missing side $x$ is 6 cm. Since the problem asks to round to the nearest tenth, the answer is $6.0$ cm.