I've done this already, but just for you I'll be happy to do it again.
The FE model assumes the sun to be 3000 miles from the face of the Earth i.e. the perpendicular distance to the Earth is 3000 miles.
Our aim is to determine the distance to the observer of the point
X at which the sun (
S) is directly overhead (i.e. the distance to the point on Earth where the sun is 90 degrees from the horizon). We may also determine the actual distance to the sun itself, though this is less relevant to the argument at hand.
We can, using the perpendicular distance to the ground of the sun, construct a right-angled triangle with the sun (
S) at one vertex and the observer (
O) and point
X at the other two:
The distance S->X is 3000 miles. The angle at O is 2 degrees, so the ratio of the distance SX to OX is tan(2) (this is the opposite side divided by the adjacent side).
If SX/OX = tan(2) where we know SX and tan(2), we can rearrange for OX to obtain:
OX = SX/tan(2) which gives the distance as 3000/0.0349207695 which equals approximately
85,909 milesWe therefore conclude that when the sun is at this angle (nearly 4 times its own angular size from the ground) it is above a point 85,909 miles away. This shows that the sun must have traveled well outside the inhabited portion of the FE just to set, which is totally inconsistent with observation. In fact, it would be impossible for parts of the FE to simultaneously receive daylight and others darkness with this arrangement, and the sun would never be observed directly overhead.