1. **State the problem:** You are in a hot air balloon 600 feet above the ground, looking down at a friend who is 1000 feet horizontally from the point directly under the balloon. We need to find the angle of depression from you to your friend. 2. **Identify the right triangle:** The vertical height is 600 feet, and the horizontal distance is 1000 feet. The angle of depression is the angle between the horizontal line from your eye level and the line of sight to your friend. 3. **Use the tangent function:** The tangent of the angle of depression $\theta$ is the ratio of the opposite side (height) to the adjacent side (horizontal distance): $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{600}{1000}$$ 4. **Calculate the angle:** $$\theta = \tan^{-1}\left(\frac{600}{1000}\right) = \tan^{-1}(0.6)$$ 5. **Evaluate the inverse tangent:** Using a calculator, $$\theta \approx 30.96^\circ$$ 6. **Interpretation:** The angle of depression from you to your friend is approximately $30.96^\circ$.