1. The problem is to find the value of $x$ in a triangle where the sides are given as 23, 34, and $x$. 2. We assume this is a right triangle and use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse (the longest side). 3. Since 34 is the largest side, we set $c = 34$, and the other sides are 23 and $x$. 4. Substitute the known values: $$23^2 + x^2 = 34^2$$ 5. Calculate the squares: $$529 + x^2 = 1156$$ 6. Isolate $x^2$: $$x^2 = 1156 - 529$$ 7. Simplify: $$x^2 = 627$$ 8. Take the square root of both sides: $$x = \sqrt{627}$$ 9. Simplify the square root if possible. Since 627 = 9 * 69, and $\sqrt{9} = 3$, we have: $$x = 3\sqrt{69}$$ 10. Therefore, the value of $x$ is $3\sqrt{69}$, approximately 24.9.