Let's see what can be done with one observation.
Where was the sun on Dec 26? 5 days after the solstice, so somewhere near the southern tropic, 23.4 S.
The sun is always at 90 degrees elevation from some point on earth, and this point moves between the tropics, 46.8 degrees over half of a 365.25 day year. As a first approximation, the point of 90 degree elevation moved 1.3 degrees in 5 days. That puts it over 22.1 S latitude.
If the earth were flat, the sun, the point at 22 S latitude, and the point at 42 N latitude would form a right triangle.
What would be the distance from 42 N to 22 S latitudes, or 64 degrees? One degree of latitude is 69 miles, so that's approximately 4420 miles.
On a flat earth, a 26 degree elevation angle would put the distance from the earth surface to the sun at 4420 * tan (26) = 2160 miles.