Q.Star A is farther than star B. Which star will have a large parallax angle?

The parallax method is the standard technique for measuring distances that are too large to reach with a metre scale — distances of planets, stars, and other astronomical objects — and, run in reverse, for measuring the sizes of such objects once their distance is already known.

Parallax itself is the apparent shift in an object's position that occurs purely because the observer's own position has changed — you can see this yourself by looking at your own hand alternately with your left eye and then your right eye closed; the hand appears to shift against the background, even though it hasn't moved at all. For astronomical distances, this idea is scaled up: instead of two eyes, two widely separated observation points (on the Earth's surface, or — for even more distant stars — two points on opposite sides of the Earth's orbit around the Sun, a baseline of 2 astronomical units) are used to sight the same object simultaneously. If $b$ is the known baseline between the two observation points and $\theta$ is the measured parallax angle (the angle between the two lines of sight, as seen from the object), then the object's distance is $D = b/\theta$ (with $\theta$ in radians) — because for a very distant object, $b \ll D$, and the angle is small enough that the arc and the straight baseline are essentially the same length.

Three special units of astronomical distance follow naturally from this method: the astronomical unit (AU), the mean Earth–Sun distance ($1.496\times10^{11}$ m); the light year, the distance light travels in one year ($9.467\times10^{15}$ m); and the parsec, defined as the distance at which a baseline of exactly 1 AU would subtend a parallax angle of exactly 1 arcsecond ($3.08\times10^{16}$ m $\approx 3.26$ light years) — a unit purpose-built to make parallax-based distance calculations simple.

Once an object's distance $D$ is known this way, the same small-angle geometry, run in reverse, gives its physical size: if $\alpha$ is the object's measured angular diameter (the angle its full width subtends, as seen through a telescope), then its true diameter is $d = D\alpha$. This angular-diameter technique is how astronomers find the actual physical size of planets and stars whose distance has already been pinned down by parallax — and, at the very smallest end of the length scale, atomic and nuclear sizes need an entirely different toolkit (electron microscopy, using the tiny wavelength of accelerated electrons), since no angular or parallax method can resolve distances that small.