You are standing on a beach looking out into the ocean. Assuming your view is unobstructed, how far can you see?
Let R be the radius of the earth, and let h be the distance from the ground to my eyes. The center of the earth, my eyes, and the furthest point I can see form a right triangle with hypotenuse (R+h) and with one leg R. The distance I can see is the length of the other leg, which is sqrt((R+h)^2 - R^2) = sqrt(2Rh+h^2).
Solution
