Answer
$\theta = 30^{\circ}$
Work Step by Step
When unpolarized light passes through a polarizing filter, the intensity of the transmitted light is $0.5~I_0$ where $I_0$ is the original intensity.
Thus the intensity is $I_1 = 175~W/m^2$ after passing through the first polarizing filter.
We can find the angle from vertical of the second polarizing filter:
$I_2 = I_1~cos^2~\theta$
$\frac{I_2}{I_1} = cos^2~\theta$
$cos^2~\theta = \frac{131~W/m^2}{175~W/m^2}$
$cos^2~\theta = 0.7486$
$cos~\theta = \sqrt{0.7486}$
$cos~\theta = 0.865$
$\theta = cos^{-1}~(0.865)$
$\theta = 30^{\circ}$
