Answer
$\theta_{2}=21.78^{\circ}$
Work Step by Step
Use Snell's Law, $\frac{c_{1}}{c_{2}}=\frac{\sin\theta_{1}}{\sin\theta_{2}}$ to solve for $\theta_{2}$.
For this exercise we can assume,
$c_{1}=3 \times 10^{8} m/s$ (the speed of light in the air)
$c_{2}=2.254 \times 10^{8} m/s$ (the speed of light in water)
$\theta_{1}=29.6^{\circ}$
Substituting in the formula,
$\frac{c_{1}}{c_{2}}=\frac{\sin\theta_{1}}{\sin\theta_{2}}$
$\sin\theta_{2}=\sin\theta_{1}*\frac{c_{2}}{c_{1}}$
$\theta_{2}=\sin^{-1}(\sin\theta_{1}*\frac{c_{2}}{c_{1}})$
$\theta_{2}=\sin^{-1}(\sin(29.6^{\circ})*\frac{2.254 \times 10^{8}}{3 \times 10^{8}})$
$\theta_{2}=\sin^{-1}(0.3711)$
$\theta_{2}=21.78^{\circ}$
