Final answer:
To see the Big Dipper and the star Polaris arranged at a 45-degree angle, you would need to wait for about 3 hours and 20 minutes from 8pm.
Step-by-step explanation:
In order to answer your question, we need to understand how the position of the stars in the night sky changes due to Earth's rotation. At 8pm, when the Big Dipper and the star Polaris are arranged in a vertical line, they are aligned with the north celestial pole. However, as the night progresses, the stars appear to move due to Earth's rotation. To see them arranged at a 45-degree angle to the vertical, you would need to wait for about 3 hours and 20 minutes. By around 11:20pm, give or take a minute or so, you would see the Big Dipper and Polaris arranged at a 45-degree angle.