surveying
posted by parker .
on a lake without any waves, how far from the shore is a sailboat when the top of 10 m mast disappears from view of a person whose eye height is one m above the water's edge

The distance D to the horizon in km by an observer at H m from the ground is given approximately by
D=3.56√H
The visible distance between two objects at H1 and H2 away from (the same) horizon is thus given by the sum of the distances, namely:
D=3.56(√H1+√H2)
=14.83 km.
See
http://en.wikipedia.org/wiki/Horizon
Follow the derivation of the formula to understand the geometry behind it.