I have produced an error in the results. If I devided 925km by tan of 7.2 degrees I get 7,322km or 4,497 miles. Using your 200m value I obtain 1,000km Syrene-Alexandria distance, which divided by tan of 7.2 degrees, I obtain 7,916km or 4,861 miles. thus the 185m to 200m vlue estimate for a stadiom has to be way off for the distance of the sun to earth to be 3,000 miles.

Also, refraction can alter your results since the light from the sun passes through a medium of the atmosphere thus bending light.