# measurement of horizon?

A person of height 1.35 meters is looking toward the horizon. The radius of the Earth is 6380000 meters. What is the distance from the person to the horizon in meters?

### 4 Answers

- RaymondLv 74 weeks agoFavourite answer
If this is a homework question in geometry, then draw the triangle.

The height of the person's eye = radius of Earth + height of the person.

Call it Rh = R + h = 6 371 000 + 1.35

Rh = 6371001.35

The horizon is the point where the person's view is tangent to the surface; the line from the person's eye to the Earth's circumference makes a right angle (90 degrees or pi/2 radians, as you wish) with the line from Earth's centre to that point (therefore, the radius.

This gives you a right-angle triangle with the hypotenuse being Rh and the side from Centre to surface being R.

Cosine angle = adjacent / hypotenuse = R / RH

This angle is at Earth's centre.

Cos(angle) = 6371000 / 6371001.35 = 0.999999788...

The arcCos of that (inverse of cosine) = an angle of 0.000650996 radians

--"Why radians?"

Because a radian is a fraction of the radius, measured along the circumference.

The distance to the horizon =

Radius * angle in radians

6371000 * 0.000650996 = 4147.4966 m

or

4.147 km

Before the invention of electronic calculators, we did not bother with such a calculation. We relied on approximations. The one I remember is

Distance to horizon (in nautical miles) = 1.1 sqrt(height in feet)

A nautical mile is 1862 m

More recent approximations (as found in other answers) do take into account the air refraction (the horizon you "see" is a tiny bit further out, because the air "bends" the path of light from that point to your eye). That is why 4.48 is not a bad answer.

- Ronald 7Lv 74 weeks ago
Around 15, 000 Meters or 15 Kilometers to be correct

11 Miles

Source(s): And proof if needed for certain Idiots that the Earth is a Globe - billrussell42Lv 74 weeks ago
Distance to horizon is d = 1.323√h

d in miles and h in feet

or d = 3.856√h

d in km and h in meters

d = 3.856√1.35 = 4.48 km

- Anonymous4 weeks ago
Bring me the horizon and I shall measure.