1. **Problem statement:** A piste is 1200 meters long down the mountain with a height difference of 450 meters. We need to find the horizontal distance (a) and the steepness of the slope in percent (b). 2. **Formula used:** This is a right triangle problem where the piste is the hypotenuse ($c=1200$ m), the height difference is one leg ($a=450$ m), and the horizontal distance is the other leg ($b$). By Pythagoras' theorem: $$b=\sqrt{c^2 - a^2}$$ 3. **Calculate horizontal distance:** $$b=\sqrt{1200^2 - 450^2} = \sqrt{1440000 - 202500} = \sqrt{1237500}$$ 4. **Simplify:** $$b=\sqrt{1237500} \approx 1112.48 \text{ meters}$$ 5. **Calculate steepness in percent:** Steepness is the ratio of height difference to horizontal distance times 100: $$\text{Steepness} = \frac{450}{1112.48} \times 100 \approx 40.46\%$$ **Final answers:** - Horizontal distance is approximately $1112.48$ meters. - The steepness of the slope is approximately $40.46\%$.