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?

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  • 4 weeks ago
    Favourite 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.

  • 4 weeks ago

    Around 15, 000 Meters or 15 Kilometers to be correct

    11 Miles

    Attachment image
    Source(s): And proof if needed for certain Idiots that the Earth is a Globe
  • 4 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

  • Anonymous
    4 weeks ago

    Bring me the horizon and I shall measure. 

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