Q&A for How to Calculate the Distance to the Horizon

Not the entire object, but you might be able to see part of it if it's tall enough. If something like a tree or a building is standing just beyond the horizon, you might be able to see the upper part of it.

The trees in the forest or the buildings in the city would affect the view.

Because there are 43,560 square feet in an acre, 630 square feet equal 630 / 43,560 = 0.01446 acre.

Yes. One modern way is by using radar, but a more traditional way is by using trigonometry and parallax. Measure out a straight baseline along the ground, and carefully measure the angle between this baseline and your distant object from each endpoint of your baseline. One then has two angles and their included side, so it is now possible to solve for the missing lengths: a = L * sin(A)/sin(A+B) where L is the length of your baseline, A and B are your two measured angles, and "a" at the distance along the side opposite angle A (i.e., between the point at angle B and the distant object).

1.17 X the square root of height of eye = distance to the horizon in nautical miles. Maybe 3 miles if you are standing in a boat and 9 feet above the water.

You are correct that the formula seems to be missing a sin. Perhaps the authors intend to use the small angle approximation (sin x ~ x) which is good enough for this sort of calculation, but only works if your calculator is in radians mode when you do the arccos. To avoid misleading readers, they should have either explicitly specified radians, or used your formula where it doesn't matter how angles are measured.

My statement was in error. The 89 mile reference pertained to a higher observation point above the ground or ocean. 3 miles is correct.

1.17 X the square root of height of eye = distance to the horizon in nautical miles.

Receiving a TV signal from 900 miles away is not realistic; most signals travel 100 miles or less. The required height of your antenna depends on factors like the power of the transmitter, the elevation of the broadcast antenna, your antenna's efficiency, and any obstructions like mountains between the antennas.

Use inches or centimeters.

You cannot calculate the angle, but you can measure it using a tool called a sextant.

No, the Earth is nearly a perfect sphere, so you can see roughly the same distance in any direction, assuming no obstacles like mountains or valleys. A great circle route is the shortest distance between two far-apart points on a sphere and doesn't apply to the relatively short distance to the horizon.