For most applications, a simple approximation to within about 1%, which is close enough for most situations on Earth is:
D (Nautical Miles) = Square root of Height (Feet).
So to answer 'effortless's original question, the distance visible from 35,000' is around 190NM or 220 miles, not 700 miles. Apologies for making it appear so simple, when it can be made to sound so mathematically involved and over-complicated.