Dist = sqrt(2Rh + h*h)
is this a derivation from radian measure along an arc?

Nope. Just a little Pythagorean Theorem (a^2 +b^2 = c^2).

To help visualize it, begin with a circle of radius R. That radius
becomes one leg of a right triangle and the radius + h (h is the
height above the surface) becomes the hypotenuse. Let x be the unknown
leg of the triangle (the distance to the horizon).

So:

a^2 +b^2 = c^2

R^2+x^2=(R+h)^2

Solve for x

x^2=R^2+2Rh+h^2-R^2

x=sqrt(2Rh+h^2) or x=sqrt(2Rh+h*h)

Errol