How tall should a skyscraper in St. Louis be to see both the Pacific and Atlantic Oceans from its roof?

Assume perfect visibility for climatic conditions and clear line of sight.

For simplicity, let's assume St.Loius is in the middle and that it's 1600 miles from there to those oceans. If the radius of the earth is 4000 miles, the distance subtends and angle of 1600/4000 radians = 0.4 radians. Let h be the required height. Then

cos(0.4 radians) = 4000 / (4000+h)

from which h = 343 miles