next time you're in the flatlands . . .
At Bonneville Salt Flats (Great Salt Lake, Utah) one can stand on the Interstate and look east at the endless row of telephone poles gradually shortening with distance around the Earth. Last one disappears about 30 miles out (or so I used to teach it) if visibility is good enough (that is, nearly every day).
That's 6' of you and 45' of pole, the math gets daunting. Want more? Go to a coffee shop near your favorite university, look around for a female math major, offer her a coffee for a brief expansion. Soon you'll be involved in interesting research other than mathematical . . .
OR: Any text on the (sadly) obsolete art of celestial navigation will have correction tables for "dip." (But then you'd have to convert the angular-error-to-the-horizon into feet-of-height. Hey, are you still awake out there? Wake up!)