HMMT 2018 U12

$\triangle P N R$ has side lengths $P N=20, N R=18$, and $P R=19$. Consider a point $A$ on $P N . \triangle N R A$ is rotated about $R$ to $\triangle N^{\prime} R A^{\prime}$ so that $R, N^{\prime}$, and $P$ lie on the same line and $A A^{\prime}$ is perpendicular to $P R$. Find $\frac{P A}{A N}$.