1. **State the problem:** We have a right triangle with hypotenuse $25$ and one leg $21$. We need to find the length of the other leg $x$ using the Pythagorean theorem. 2. **Formula:** The Pythagorean theorem states that in a right triangle, $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse and $a$, $b$ are the legs. 3. **Apply the formula:** Here, $c = 25$, one leg $b = 21$, and the other leg is $x$. So, $$x^2 + 21^2 = 25^2$$ 4. **Calculate squares:** $$x^2 + 441 = 625$$ 5. **Isolate $x^2$:** $$x^2 = 625 - 441$$ $$x^2 = 184$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{184}$$ 7. **Simplify and approximate:** $$x \approx 13.6$$ (rounded to the nearest tenth) **Final answer:** $$\boxed{13.6}$$