# surveying

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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

• surveying -

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.

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