Let O be the center of the earth. Triangle OAS is a right-angle triangle since SA is tangent to the earth, which we consider to be a perfect sphere.

We thus have OS^{2} = OA^{2} + AS^{2}

but OA = 40,000,000/(2pi) meters

and OS = OA + 125.7 = OA + 40pi/OS^{2} ~= OA*OA + 2 OA = 40pi

Consequently,

AS = sqrt(OS^{2} - OA^{2}) ~=
sqrt(2*40pi^{.}40,000,000/2pi) = 40,000 m
The horizon is therefore approximately 40 km from the top of the lighthouse.

Source: Berrondom, Marie

Categories: Geometry and Space

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