I have an obsession with geometry, and have in the past looked for a good free geometry program, and come up with some reasonable ones in the past. But this prompted me to look again, and I found a great one: GeoGebra.

Anyway, I created a diagram for this problem. It's saved in the attachment. If you assume that the earth has a circumference of 40,000km, a mountain would have to be over 7.29 miles high in order to be seen, ignoring atmospheric refraction.

Oh, and GeoGebra let me create sliders so that I can manipulate the circumference and distance. It also let me know that a 2m viewing height is nearly irrelevant.