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If you were to stand on a tall building in Washington, DC and looked west, how tall would the building need to be to see Los Angeles? I would like answers based on if the world was flat and if the world was round. The distance is 2300 miles from Washington, DC to Los Angeles, California. According to Visual Line of Sight Calculations, the Earth's curvature has an average curvature of 7.98 inches per mile.

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  • $\begingroup$ If you can help edit this question please do so. $\endgroup$ Nov 22, 2015 at 20:24

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The website you provide a link for gives the horizon distance as:

$d$ $\approx$ $1.23\sqrt{h}$

where d is in miles and h is height above ground level in feet.

Rearranging the equation

$h$ $\approx$ $(d/1.23)^2$

For a horizon distance of 2300 miles, the height would have to be 3,496,596 feet, or 662.2 miles.

For a flat Earth, it depends on the height of any obstacles between Washington DC & LA and the distance the obstacle is from either LA or Washington. If there are no obstacles, no height is required as light from LA can travel across the flat plane to Washington.

If you want to account for impedance provided by the Rocky Mountains, use Google Earth & draw a line between LA & Washington. A high point of around 9600 feet occurs some 780 miles from LA.

By using similar triangles such a height at Washington would be 28,308 feet.

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    $\begingroup$ Good answer, I would say that would explain what I need to know completely $\endgroup$ Nov 23, 2015 at 3:23
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    $\begingroup$ Feet? Miles? What is this, 1990? $\endgroup$
    – Gimelist
    Nov 23, 2015 at 7:37
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    $\begingroup$ @Michael: I'm assuming that as with me, for you the metric system is second nature. I find the "old" units awkward & archaic, but this is an international site and not all countries use the metric system. The question & the linked site used non metric units, so I used "old" units in the answer. $\endgroup$
    – Fred
    Nov 23, 2015 at 7:46
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    $\begingroup$ This equation is only correct for small values of h (where "small" is relative to the diameter of the earth). For instance, plugging in a height of 265 million kilometers gives you a horizon distance of 20k km, which means you can see the opposite side of the earth, which is obviously impossible. $\endgroup$ Nov 23, 2015 at 22:25
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    $\begingroup$ @fred that's an unusual way of putting it... this is an international site and... I can only think of one country that doesn't use the metric system :-) $\endgroup$ Nov 25, 2015 at 0:45

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