Answer
$\theta = 28.1^{\circ}$
Work Step by Step
Note that the refraction angle as the ray enters material 2 is $~~\theta_2 = (90.0^{\circ}-\phi)~~$ which is $~~\theta_2 = 30.0^{\circ}$
We can find use Snell's law to find $\theta$:
$n_1~sin~\theta = n_2~sin~\theta_2$
$sin~\theta = \frac{n_2~sin~\theta_2}{n_1}$
$\theta = sin^{-1}~(\frac{n_2~sin~\theta_2}{n_1})$
$\theta = sin^{-1}~(\frac{1.60~sin~30.0^{\circ}}{1.70})$
$\theta = sin^{-1}~(0.4706)$
$\theta = 28.1^{\circ}$
