You are in a hot air balloon, 200 m above the flat texas plains. you look out towards the horizon. how far out can you see- that is, how far is your horizon? the earth's radius is about 6400km.

Radius of earth as given in question = 6400 km
Height of the air balloon = 200 m
                                       = 0.20 km
Now
Let us assume the distance up to which one can see from the balloon = d
Then
d=sqrt [(R+h)2−R2] 
  = sqrt [2Rh+h^2]
  = sqrt [2 (6400 * 0.20) + (0.20)^2]
  = sqrt [(2 * 1280) + 0.04]
  = sqrt [ 2560 + 0.04]
  = sqrt [2560.04]
  = 50.6 km
A person in the balloon can see up to a distance of 50.6 km. I hope the answer has helped you.

Its in the national history museum and you can't se the original because its locked away in a vault 

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