Distance computation?

Question

If you know your height above the ground, how far away is the horizon, or how can compute the distance to the horizon?

Answer 1

Let r=the earth's radius and h=your height.

Draw a right triangle ABC, where AC = length r, BC = length r+h, and
length(BA) = sqrt((r+h)^2 - r^2)
= sqrt(2rh + h^2).

Answer 2

Basically, you form a right triangle with the information that is given. and label the distance to the horizon as variable X. Then you use trigonometry to figure out the answer. I think you may be missing some information, like the angle from the ground at which the point above the ground is. Or, if you have two of the three sides, you can use the Pythagorean theorem. (a^2+b^2=c^2, where c squared is the hypotenuse of the triangle). Hope that helps, and it's not too confusing!

Answer 3

Not sure I understand what the "horizon" is. If it's an object in the distance, and you know the distance to the "horizon" when you're on the ground, and you know how far above the ground you are, then your distance to the "horizon" is just the hypotenuse of a right triangle. Then the distance to the "horizon" would be the square root of the height above the ground squared plus the distance to the horizon on the ground squared.

Answer 4

If your eyes are H feet above ground level, the distance to the horizon is approximately sqrt(3 * H / 4) miles. If there is an object on the horizon above ground level, you can add the two distances.

For example, ship's bridge 50 feet above sea level, horizon distance 6.1 miles; lighthouse 150 feet above sea level, horizon distance 10.6 miles; the ship's lookout can JUST see the lighthouse from 16.7 miles away (its top appears on his horizon).