If the straight line through the point P(3, 4) makes an angle $\frac{\pi }{6}$ with the x-axis and meets the line 3x + 5y + 1 = 0 at Q, the length PQ is

               $P\left(3,4\right)\theta =\pi /6$

                $3x+5y+1=0$

                $PQ=r=\left|\frac{a{x}_1+b{y}_1+c}{a\cos \theta +b\sin \theta }\right|$

                $=\frac{30\times 2}{5+3\sqrt{3}}$

                $=30\left(3\sqrt{3}-5\right)$