Final answer:
Parallax is used to determine distances to nearby stars by measuring shifts in their positions, with larger parallax angles for closer stars. Distances beyond a certain range cannot be accurately measured because the angles become too small.
Step-by-step explanation:
Parallax is a method used to determine distances to nearby stars by measuring the shift in position of a star relative to very distant background objects when observed from two different points in Earth's orbit around the Sun, six months apart. The true parallax is defined as half of the observed angular shift to work with a baseline of 1 Astronomical Unit (AU), the average distance between the Earth and the Sun, instead of 2 AU.
The nearest stars to Earth exhibit the largest parallax angles, and as the distance increases, the parallax angles decrease and become too small to measure accurately beyond a certain distance. This is why accurate parallax measurements are not feasible for very distant stars. With advancements in technology, such as the Hipparcos satellite and the Gaia mission, accurate parallax measurements can be made for stars out to approximately 300 light-years and potentially up to 30,000 light-years respectively.
Regarding the options provided: A) is not accurate because nearby stars have the largest parallax angles, not the 'samples'; B) is true, distant stars have parallax angles that can be too small to measure; C) is true, it is used to measure distances to stars; and D) is not fully correct because both A and B are not true as A is a misstatement. Therefore, the correct responses are B) and C).