Problem

The key is to write the line through $P$ using its angle of inclination, then find where it intersects the given line. A line making angle $\theta$ with the $x$-axis has slope $m = \tan(\theta)$, so you can express it in parametric form: points along the line are at distance $t$ from $P$ along the direction $(\cos\theta, \sin\theta)$. Substitute into the equation of the second line to solve for $t$—that's your distance $PQ$.

The key is to write the line through $P$ using its angle of inclination, then find where it intersects the given line. A line making angle $\theta$ with the $x$-axis has slope $m = \tan(\theta)$, so you can express it in parametric form: points along the line are at distance $t$ from $P$ along the direction $(\cos\theta, \sin\theta)$. Substitute into the equation of the second line to solve for $t$—that's your distance $PQ$.