How far is it to the horizon?

Question

A 5' 6" tall woman is standing on a hill (Elev. 30 ft above sea level). She is looking into the distance of the ocean in front of her and wonders how far it is to the horizon. (This is a very smart woman, so that the distance from the top of her head to the center of her eyes measures 6").

Without using a calculator and without using trigonometry, what is the approximate distance to the horizon ? Does anyone know how to solve this problem?

Answer 1

For your woman, the distance to the horizon is 7.2475 miles (11.663 7 kilometers).

The formula for distance from the viewpoint to the horizon on any sphere is

d = (√(2Rh)) + (h^2). R is the radius (of the Earth or any sphere). h is the height of observer. d is the distance from observer to horizon.

All calculations depend on the water's surface being completely smooth, no waves! ~Sounds like a very calm day.

Using this a person with eye level at 5 feet 8 inches above water could see 2.92 miles.

Metric: 1.73 meters and 4,695.06 meters.

If you are standing on a hill 100 feet above the water, the horizon is 12.25 miles away.

Metric: 30.48 meters and 19,707.29 meters.

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