#### Answer

(a) $c_{2}$ = 2.148 x $10^{8}$ $\frac{m}{s}$

#### Work Step by Step

For this problem, we use the following information:
$\frac{c_{1}}{c_{2}}$ = $\frac{\sin\theta_{1}}{\sin\theta_{2}}$
$c_{1}$ = 3 x $10^{8}$ $\frac{m}{s}$
Now, we want to express the equation in terms of $c_{2}$.
1. $\sin\theta_{2}$ $\times$ ($\frac{c_{1}}{c_{2}}$) = $\sin\theta_{1}$
2. ($\frac{\sin\theta_{2}}{\sin\theta_{1}}$) $\times$ $c_{1}$= $c_{2}$
From here, we can plug in the values to solve for $c_{2}$
(a) $\theta_{1}$ = 46$^{\circ}$ $\theta_{2}$ = 31$^{\circ}$
$c_{2}$ = $c_{1}$ $\times$ ($\frac{\sin\theta_{2}}{\sin\theta_{1}}$)
$c_{2}$ = 3 x $10^{8}$ $\times$ ($\frac{\sin 31^{\circ}}{\sin 46^{\circ}}$)
$c_{2}$ = 2.148 x $10^{8}$ $\frac{m}{s}$