Well, someone ad to do it...
Imagine a triangle between you, the earths centre and the point on the horizon you wish to find the distance of. You have a right angle triangle. (your line of sight is a tangent to the circle of the earth, therefore forming a right angle with its radius)
Assuming:
1. the earth has a uniform radius of 3440.227 nautical miles
2. the earth is perfectly round (and no mountains)
3. you can actually see farther than your radome
Here's my 'guess' of how far it is to the horizon:
1000ft = 33nm
2000ft = 48nm
5000ft = 75nm
10,000ft = 106nm
20,000ft = 150nm
30,000ft = 184nm
40,000ft = 213nm
and to confirm CATCHUP's comment, my calculations say...
ISA Tropopause @ 36,000ft = 202nm
There you go, it's time for bed now!!
DAMN YOU PIETER PAN!!