Really Hard Math Question

Question

Willis Tower (formerly Sears Tower) is 1451 ft tall, with the Skydeck (observation deck) at 1353
feet. The advertising literature for the Skydeck claims a person can see for 40 – 50 miles. Imagine
it is a clear day and you look out over Lake Michigan from the Skydeck. How many miles can he
actually see? Assume the radius of the earth is 3960 miles. Caution, the distance is to be measured
along the curvature of the earth.

Answer 1

I am accepting a premise found at the following website link that for a 6' person, given the curvature of the earth, the horizon - the farthest place that you can see is 3 miles on flat level ground.

 

http://www.livescience.com/32111-how-far-away-is-the-horizon.html

 

This same website says that if you stood atop Mount Everest at 29,029 feet in elevation, you would see about 230 miles.

 

If we accept that premise then at 1353 plus 6' for the man on the observation beck then one could see 10.76 miles or 11 miles if we simply round the answer up.....

 

Its a simple ratio or percentage at 1359 feet.....good question!