What if we didn't know the distance to the Sun? The DISTANCE is crucial to accurately determining characteristics of Stars (and just about everything). An important method includes
Parallax
Consider the triangle above. If we know the baseline (orbital size of the Earth), and we measure the angle centered on the Star (the parallax angle), we can determine the distance using the small angle formula.
Parsec
The distance of a star which subtends an angle of one arcsecond over one Earth orbit. It is
approximately 3.26 light years.
Ancient Greeks knew enough geometry to test a theory that the earth goes around the Sun and to look for parallactic motion of the stars. They saw NONE and concluded the Earth stood still. However, the parallactic motion of even the closest stars is so small, it is simply unobservable with an unaided eye! The Earth IS moving!