# How is the size of earth measured?

The arc to the visible horizon, from height h subtends an angle $\theta$, at the center of Earth, The Earth radius r is given by the implicit formula $\cos \left(\theta\right) = \frac{r}{r + h}$.
The angle $\theta$ can be obtained from the arcual distance s of the visible horizon and r, using
$\theta$ radian = s / r.
There are iterative numerical methods to solve this r-implicit equation cos$\left(\theta\right) = \frac{r}{r + h}$, using a starter (estimated) value for r.