Consider the earth as the perfect spheroid
and assume it's surface to be completely land. A person whose eyes are 2 meters above the ground is randomly placed on the earth facing a random direction. What is the expected sight distance of this person?
Sight distance is defined as follows.
A ray is drawn from the person's eyes in the direction he/she is facing such that it is tangent to the spheroid at point B. The linear distance from the person's eyes to point B is the sight distance.
I just thought of this problem today and I have no clue how difficult it is. Approximations are welcomed (for example, calculating the expected distance from the person's feet to point B.