1. **State the problem:** We need to find the value of $x$ in a right triangle where the sides given are 23 and 34, and $x$ is the unknown side. 2. **Identify the formula:** In a right triangle, the Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse (the longest side), and $a$ and $b$ are the other two sides. 3. **Determine which side is the hypotenuse:** Since 34 is greater than 23, 34 is likely the hypotenuse. 4. **Set up the equation:** Let $x$ be the other leg. Then: $$x^2 + 23^2 = 34^2$$ 5. **Calculate squares:** $$x^2 + 529 = 1156$$ 6. **Isolate $x^2$:** $$x^2 = 1156 - 529$$ $$x^2 = 627$$ 7. **Find $x$ by taking the square root:** $$x = \sqrt{627}$$ 8. **Simplify the square root if possible:** 627 factors as $9 \times 69.666...$ but 9 is a perfect square, so: $$x = \sqrt{9 \times 69.666...} = 3 \sqrt{69.666...}$$ Since 69.666... is not a perfect square, leave as is or approximate. 9. **Approximate the value:** $$x \approx 3 \times 8.35 = 25.05$$ **Final answer:** $$x \approx 25.05$$