Question

You are in a hot air balloon, 100 m above the flat Texas plains. You look out toward the horizon.
How far out can you see-that is, how far is your horizon? The Earth's radius is about 6400 km.
Express your answer using one significant figure.

Answer 1

Actually we could create a triangle in this case. The hypotenuse is the radius of Earth plus the height above the earth, while the two sides are the radius of Earth and the scope of vision.

 

That is:

(6,400,000 m + 100 m)^2 = (6,400,000 m)^2 + b^2

b^2 = 1,280,010,000

b = 35,777.23 m

 

You can see 35,777.23 m far.