1. **State the problem:** We need to find the value of $x$ in a right triangle where the hypotenuse is 18, one leg is 12, and the other leg is $x$. 2. **Formula used:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse, and $a$, $b$ are the legs. 3. **Apply the formula:** Here, $c = 18$, one leg $a = 12$, and the other leg $b = x$. So, $$12^2 + x^2 = 18^2$$ 4. **Calculate squares:** $$144 + x^2 = 324$$ 5. **Isolate $x^2$:** $$x^2 = 324 - 144$$ $$x^2 = 180$$ 6. **Find $x$ by taking the square root:** $$x = \sqrt{180}$$ 7. **Simplify the square root:** $$\sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5}$$ 8. **Calculate decimal value:** $$x \approx 6 \times 2.236 = 13.416$$ 9. **Round to the nearest tenth:** $$x \approx 13.4$$ **Final answer:** $x = 13.4$