Alice had been standing on the ground (Point A) and observing a brightly colored object resembling a bird on the top of a tree at a distance of 40 meters from the tree. She decided to get a closer look by moving 20 meters closer to the tree (Point B). After moving closer, she realized that the object was not a bird but something that she could catch. Then, she decided to catch it by climbing the tree, which had a height of 60 meters from the ground.

Using the above scenario, please answer the following questions showing step by step calculations and stating the formulae.

(i) Find the angles formed by Alice at the points A and B relative to the top of the tree. What are these angles called as?

(ii) Determine whether angle A is larger than angle B. Make a conclusion about the comparison of angles when observing an object from a distance versus close.

(iii) Find the distances between the object and points A and B.