1. **State the problem:** A 50-foot tree is cut 10 feet above the ground. The top part falls and forms a triangle with the ground and the remaining tree. We need to find the angle formed at the cut point. 2. **Identify the triangle sides:** The tree is 50 feet tall, cut 10 feet above the ground, so the remaining vertical part is 10 feet. The fallen top part is 40 feet (50 - 10). The fallen top touches the ground, forming a right triangle with the ground and the remaining tree. 3. **Label the triangle:** Let the angle at the cut point be $\theta$. The vertical side adjacent to $\theta$ is 10 feet. The hypotenuse (fallen top) is 40 feet. The base is unknown but not needed to find $\theta$. 4. **Use cosine function:** $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{10}{40}$$ 5. **Simplify the fraction:** $$\cos(\theta) = \frac{\cancel{10}}{\cancel{40}} = \frac{1}{4}$$ 6. **Find the angle:** $$\theta = \cos^{-1}\left(\frac{1}{4}\right)$$ 7. **Calculate the angle:** Using a calculator, $$\theta \approx 75.5^\circ$$ **Final answer:** The angle formed where the tree was cut is approximately **75.5°**.