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The distance to the horizon depends on the altitude of the observer. Assuming that the earth is a sphere and that the horizon is at sea level, the geometry of the situation involves a right triangle with the hypotenuse equal to the radius of the earth plus your altitude (R + A) and the opposite side equal to the radius of the earth (R). Then it's only necessary to apply the Pythagorean theorem to calculate the third side:

D = sqrt( (R + A)2 - R2 ) = sqrt( 2RA + A2 )

where the radius of the earth is 6367.5 km or 6.3675 x 106 m. If you're standing on the beach looking out to sea, then A is at most a few meters, say 3 m as an example. In that case, the horizon is about 6181 m or 6.181 km away. If you're on a high bluff or on the roof of a tall building looking out to sea, and your altitude is 150 m, then the horizon would be 43,706 m or 43.706 km away. The arithmetic is slightly more complicated if the horizon is anything other than the ocean.

Another Way To Look At It:

A simple approximation formula:

The distance in miles, is the square root of one and a half times the height in feet.

So, for a six foot tall person, standing on a beach: 1.5 times their height is 9. The square root of 9 = 3. So, the horizon is about 3 miles away.

Note: This simplified formula is quite accurate, but only works if the height is in feet and the distance in miles. If you want to use height in meters and distance in kilometers, you need to change the multiplier from 1.5 to 12.74.

Q: What is the distance to the horizon?

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The distance to the horizon, d kilometres, is related to the height above mean sea level, h metres, by the approximate formula: d = 3.57*sqrt(h).

If the reference point and an object are both on the horizon then the angular distance to the object, relative to the reference point is simply the angle formed between the two rays from the observer to object and to the reference point. If either the object or reference point (or both) are not in the plane of the horizon then the appropriate rays are the projections of the rays from the observer onto the plane containing the horizon.

To get an "approximate" distance to the oceanic horizon from a particular observation point, take the square root of the height of the observation point, add 22.5%, and that will give you the distance in statute miles. For example, if your eyes were 6 feet off the ground, and you stood atop a 50' tower, your observation point would be 56'. The square root of 56' is 7.48. Add 22.5% of 7.48 (1.68) to 7.48 and you have 9.16 statute miles from your eyes to the horizon.

The "horizon" is the furthest you can see. "On the horizon" therfore refers to an object which is just in sight.

horizon 3 and horizon4

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The distance in kilometers to the horizon is the square root of (13 X observers height in meters) so for a 1.8 meter person standing on the seashore the horizon is about 5 km away. For someone on a jet at 10,000 meters the horizon is 360 km away.

The distance to the horizon from the shore depends on the height of the observer's eyes above sea level. On average, a person standing at sea level on the shore can see approximately 3 miles to the horizon. If the observer is standing at a higher elevation, such as on a cliff or in a tall building, they can see farther.

The distance ahead for the forecasts on which plans are made.

The altitude of an object in the sky is the angular distance of the object above the observer's horizon. It is measured in degrees or radians from the horizon to the object.

Almost . . ."Altitude" is the apparent angle of the object above the horizon.

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Actually, altitude is the height of an object above a specific reference point, usually the observer's horizon. It is measured in degrees, with 0 degrees being right on the horizon and 90 degrees directly overhead.

The horizon. It is the apparent line that separates the Earth from the sky, and it is visible when looking out towards the distance.

The distance to the horizon, d kilometres, is related to the height above mean sea level, h metres, by the approximate formula: d = 3.57*sqrt(h).

2 miles.Answer:The distance to the horizon on the ocean is a function of the height of the observation point. In general (and with thanks to Pythagoras) it is:d=(h(D+h))0.5 whered = distance to the horizonD = diameter of the Earthh = height of the observer above sea level

Horizon d is the point at which the observer's line of sight meets the horizon, creating a horizontal line separating the sky from the earth. It signifies the boundary where the sky appears to meet the ground or sea in the distance.