Final answer:
Trigonometric parallax is used to determine the distance to stars by measuring the shift in a star's position relative to very distant background stars as viewed from opposite sides of Earth's orbit.
Step-by-step explanation:
Trigonometric parallax is used to determine the distance to stars by measuring the shift in a star's position relative to very distant background stars as viewed from opposite sides of Earth's orbit. The angle of the line of sight to the star is measured at intervals of six months apart, and the distance is calculated using the known diameter of the Earth's orbit. This method is called triangulation or the parallax method. However, accurate measurements of parallax can only be made up to a certain distance, usually about 500 light-years, because the parallax angles become too small to measure accurately beyond that distance.