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How far away is the horizon?

geometrypythagorasestimationearth

You stand at the water's edge on a calm day. Your eyes are 1.7 metres above sea level, and the Earth's radius is about 6,371 km.

How far away is the horizon, the line where the sea seems to meet the sky? Derive a simple formula and then put in the numbers. As a follow-up, how far is the horizon from the top of a 100-metre cliff?

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Draw the Earth as a circle, your eye as a point just above it, and the line of sight to the horizon as a tangent to the circle. A tangent meets the radius at a right angle.

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