Planes fly about 6.8 miles above the earth.
Look at the pretty picture on the first page of this PDF:
https://sites.math.washington.edu/~conroy/m120-general/horizon.pdf
Hypotenuse: R+height of plane "h" = 3,900 + 6.8 = 3,906.8 miles
Leg 1: R or 3,900 miles
Leg 2: L (the variable we need to solve for, the visible distance to the horizon with a smooth globe shaped earth from a plane 6.8 miles up)
3,906.8 = √(L 2 + 3,900 2 )
Square both sides gives us...
15263086.24 = (L 2 + 3,900 2 )
We square 3,900 to get...
15263086.24 = (L 2 + 15210000)
Subtracting 15210000 from both sides gives us...
53086.24 = L 2
Taking the square root of 53086.24 gives us...
L = 230.404513844672757 miles
Planes fly about 6.8 miles above the earth.
Look at the pretty picture on the first page of this PDF:
https://sites.math.washington.edu/~conroy/m120-general/horizon.pdf
Hypotenuse: R+height of plane "h" = 3,900 + 6.8 = 3,906.8 miles
Leg 1: R or 3,900 miles
Leg 2: L (the variable we need to solve for, the visible distance to the horizon with a smooth globe shaped earth from a plane 6.8 miles up)
3,906.8 = √(L ^2 + 3,900 ^2 )
Square both sides gives us...
15263086.24 = (L ^2 + 3,900 ^2 )
We square 3,900 to get...
15263086.24 = (L ^2 + 15210000)
Subtracting 15210000 from both sides gives us...
53086.24 = L ^2
Taking the square root of 53086.24 gives us...
L = 230.404513844672757 miles
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