1. **State the problem:** We have a right triangle with legs 12.5 m and 22.5 m, and hypotenuse 25 m. We want to find the distance $x$, which is the vertical height from the top corner of the 12.5 m segment to the hypotenuse. 2. **Identify the formula:** The height $x$ from a right angle vertex to the hypotenuse in a right triangle can be found using the formula for the altitude to the hypotenuse: $$x = \frac{a \times b}{c}$$ where $a$ and $b$ are the legs, and $c$ is the hypotenuse. 3. **Apply the formula:** Here, $a = 12.5$, $b = 22.5$, and $c = 25$. 4. **Calculate:** $$x = \frac{12.5 \times 22.5}{25} = \frac{281.25}{25} = 11.25$$ 5. **Interpretation:** The distance $x$ is 11.25 meters. This means the vertical height from the top corner of the 12.5 m segment to the hypotenuse is 11.25 m.