) 
 :I think the confusion here is that the important difference between 2m and 200m is a factor of 100  the absolute difference of 198m is not what you use to calculate.  So, with a factor of 100 difference between 2m and 200m, the square root of 100 is 10, so the distance to the horizon increases by a factor of 10  from 5km to 50km.  Hope this makes sense  let me know if you think I'm missing something.  Thanks!    (UTC