1. **Problem Statement:** Find the length of the zip line AD in a rectangular prism where the zip line runs diagonally from corner A to opposite corner D, making a 60° angle with post AF. 2. **Understanding the figure and given data:** - The prism has dimensions: height AF = 25 ft, width = 20 ft, length = 38.4 ft. - The zip line AD connects opposite corners A and D. - The angle between zip line AD and post AF is 60°. 3. **Formula and approach:** - The zip line AD is the space diagonal of the rectangular prism. - The length of the space diagonal $AD$ is given by: $$AD = \sqrt{(length)^2 + (width)^2 + (height)^2}$$ - However, we are given the angle between AD and AF (height), so we can use the cosine of the angle: $$\cos(60^\circ) = \frac{AF}{AD}$$ 4. **Calculate length of AD using the angle:** $$\cos(60^\circ) = \frac{AF}{AD} \Rightarrow AD = \frac{AF}{\cos(60^\circ)}$$ 5. **Substitute values:** $$AF = 25, \quad \cos(60^\circ) = 0.5$$ $$AD = \frac{25}{0.5} = 50$$ 6. **Verification using the space diagonal formula:** $$AD = \sqrt{38.4^2 + 20^2 + 25^2} = \sqrt{1474.56 + 400 + 625} = \sqrt{2499.56} \approx 49.995 \approx 50$$ 7. **Answer:** The length of the zip line AD is approximately **50 feet**.