# How far is the horizon, if a 2m tall man watches to the sea?

How far is the horizon, if a $r=2 m$ tall man watches to the sea?

I have calculated that it would be even just about 6 km. if R = radius of earth( $6370 \cdot10^3$ m ). By pythagorean theorem we get. $(r+R)^2 = x^2 + R^2$ => $\sqrt((r+R)^2 - R^2) = \sqrt((2+6370 \cdot 10^3)^2 - (6370x10^3)^2) = 5048$ m ~ $5$ km = x Is this right?

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Seems correct to me. –  Bernhard Sep 24 '12 at 10:57
But if you are looking at 100 m high hill, then you get that it disappears if you are 40 km away from it looking at the sea. $\sqrt((100+6370 \cdot 10^3)^2 - (6370x10^3)^2)+5000 = 35693 + 5000 = 40000 m$ –  alvoutila Sep 24 '12 at 11:08
Related to physics.stackexchange.com/q/29878/520. –  dmckee Sep 24 '12 at 12:31