Question

How was it determined that a parsec is 3.26 light years?

Answer 1

Hint: When the distance of those objects which are present outside the solar system is to be measured then the unit of length used to do this is called parsec. 31 trillion km is the approximate value of 1 parsec.

Complete answer:
Parallax and trigonometry are used to obtain a parsec.
The length of the adjacent leg of an extremely elongated imaginary right triangle in space is taken as a parsec. The triangle is based on two dimensions - the shorter leg of the triangle whose length is one astronomical unit (the average earth sun distance) and one arcsecond which is the measure of the subtended angle of the vertex opposite that leg.
When we apply the rules of trigonometry to these two values , the unit length of the other leg of the triangle (the parsec) can be derived.
Parallax is also used to determine the value of a parsec. Half of the angular distance that a star appears to move relative to the celestial sphere as earth orbits the sun is the definition of a parallax. It can also be described as the subtended angle, from the star’s perspective, of the semimajor axis of the earth’s orbit. It is considered to be an effective way to measure the distance to nearby stars because it relies on geometry.
If the parallax angle of an object is 1 arcsecond the parsec is defined as the distance to that object.

Note:
British astronomer Herbert Hall Turner, in the year 1913, was the first person to suggest parsec. 1000 parsec is a distance that is denoted as a kiloparsec.