Answer
The parallax angle is $2.4\times 10^{-7}~radians$
The distance is 20 parsecs.
Work Step by Step
We can use this equation to find the parallax angle of the star:
$D = \frac{d}{\phi}$
(Note that D is the distance to the star, d = 1 AU, and $\phi$ is the parallax angle measured in radians.)
$\phi = \frac{d}{D} = \frac{1~AU}{65~ly} = \frac{1.5\times 10^{11}~m}{(65)(9.46\times 10^{15}~m)}$
$\phi = 2.4\times 10^{-7}~radians$
The parallax angle is $2.4\times 10^{-7}~radians$.
We can convert the distance to units of parsecs:
$D = (65~ly)(\frac{9.46\times 10^{15}~m}{1~ly})(\frac{1~pc}{3.09\times 10^{16}~m})$
$D = 20~pc$
The distance is 20 parsecs.
