How Vast Is Your Vision?

Geometry Level 5

A man with eye-to-ground height 2 meters is standing on top of Mt. Everest which is 8,848 meters high. Suppose also that Mt. Everest was "relocated" on a point in the Pacific Ocean where there are no mountains, no islands, no clouds, just the plain ocean in sight.

The spherical surface area enclosed by the horizon (neglecting the presence of the mountain) as seen by the man can be expressed in the form \[ \pi R^2 \dfrac{A}{B}, \] where \(A\) and \(B\) are coprime positive integers, and \(R\) is the radius of the Earth (assumed to be a perfect sphere with \(R = 6371\text{ km}\)).

Find \(A+B\).

Note: Assume also that the man has a maximized vision.


Problem Loading...

Note Loading...

Set Loading...