However, I do know the angular size of the Sun (as seen from Earth) is about 0.53° -- yes, the distance from the Earth to the Sun does change, but I don't mind.

You may have come across the term 'angular spreading' in the Surfline forecasts—well here's what it means.

By referring to charts that gave the star’s angular distance from the celestial equator, or declination, and determining the angle at the star, he could pinpoint his latitude.