Step 1: Make figure from the given information

Diameter of the earth OB = 3* 10^{11} m
Radius of the earth = \frac{OB}{2} = 1.5 * 10^{11} m
Parallax angle \theta = 1 ''
\theta = 1 * \frac{1}{60* 60} * \frac{\pi}{180} = 4.847* 10^{-6} radians
Distance between the earth and star = BC = d
Step 2: Using the parallax method to find the large distance (d)
Formula: Parallax angle \theta = \frac{OB}{BC}
BC = \frac{OB}{\theta}
BC = \frac{1.5 * 10^{11}}{4.847* 10^{-6}}
BC = 3.09 * 10^{16}
Hence, 1 \text{ persec } = 3.09 * 10^{16} m