The first polaroid alinsisates half the light so that the intensity is reduced by half $I^{\prime }=\frac{I_0}{2}.$ The light reaching the second polarizer is vertically polarized and so intensity is reduced to

$I"=I\prime {\left(\mathrm{c}\mathrm{o}\mathrm{s}30°\right)}^2=\left(\frac{3}{4}\right)\left(\frac{I_0}{2}\right)$

$=\frac{3I_0}{8}$

Therefore, transmitted light is plane polarised to the vertical at $30°$ and having intensity $\frac{3I_0}{8}$