1. **Problem statement:** A peacock is sitting on top of a tree 10 m high and observes a snake moving on the ground. The snake is $10\sqrt{3}$ m away from the base of the tree. We need to find the angle of depression of the snake from the peacock's eye. 2. **Formula and concept:** The angle of depression from the peacock to the snake is the angle between the horizontal line from the peacock's eye and the line of sight to the snake. This angle is equal to the angle of elevation from the snake to the peacock due to alternate interior angles. 3. **Using trigonometry:** Consider the right triangle formed by the tree height (opposite side), the distance of the snake from the base (adjacent side), and the line of sight (hypotenuse). 4. The tangent of the angle of depression $\theta$ is given by: $$\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{10}{10\sqrt{3}} = \frac{1}{\sqrt{3}}$$ 5. From trigonometric values, $\tan 30^\circ = \frac{1}{\sqrt{3}}$. 6. Therefore, the angle of depression $\theta = 30^\circ$. **Final answer:** The angle of depression is $30^\circ$.