system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How did we measured the radius of earth and sun?﻿
gpt
The circumference (and by extension the radius) of the Earth can be measured by comparing the angle of shadows of vertical objects at different latitudes (same longitude) at identical times.

The radius of the sun was a little more complicated and there are a variety of methods. One was to measure the ratio of the distance to the moon and the sun (using trigonometry during a half moon).

Based on this ratio, and the size of shadow the Earth casts upon the moon during an Eclipse, you can estimate the size of the sun. Similar and different methods have been used over the years, but they basically boil down to: shadows and math.