trig, Phoenix College
posted by Jama .
Where did the number 0.5736 come from or originated from?
Will the horizon be closer or farther away when your eyes are closer to the surface?
Will the horizon be closer or farther away when your eyes are farther from the surface?

Therefore, to determine how far in miles we can see from a building of height h ft., we use d = sqrt[1.5h].
To determine the height of a building we can see from a distance d off shore, we use h = sqrt(r^2 + d^2)  r, r and d in feet.
A sampling of some values:
h in feet....6......10.......25.......100......1000......5000....10,000......29,000.......528,000(100miles)
d in miles.2.45.3.87....6.12....12.25....38.75......86.6.....122.5........208.5............890
d in miles.1........5.......10........25.........50.........75........100..........200.............1000
h in feet..2/3...16.66....66.66..416.66..1666.66...3750....6666.66..26,666.66......666,666(126.25miles)
Does this answer your question?