Final answer:
Astronomers use the parallax angle method, which involves geometry and Earth's orbit, to measure distances to nearby stars up to 500 light-years away.
Step-by-step explanation:
The main method astronomers use to measure the distance to nearby stars is parallax angle measurement. By taking advantage of Earth's orbit around the Sun as a baseline, astronomers observe the slight shift in position of a nearby star relative to distant background stars. This shift, observed at six-month intervals, allows them to calculate the distance to the star using simple geometric principles, up to about 500 light-years (ly) away. Distances obtained through parallax measurements are a fundamental link in the chain of cosmic distances and do not rely on any assumptions, making them very reliable.