#### Answer

After 30 minutes, the cars would be $35.6\text{ miles}$ apart.

#### Work Step by Step

Let both cars start from the same point with direction difference of $80{}^\circ $.
The distance traveled by the first car in $30$ minutes is:
$60\times \frac{1}{2}=30$ miles
The distance covered by the second car in 30 minutes is:
$50\times \frac{1}{2}=25$ miles
Now the distance after 30 minutes between the cars is $AC$ if they start from point B.
Using the law of cosines we will obtain the length of AC:
$\begin{align}
& A{{C}^{2}}=B{{C}^{2}}+A{{B}^{2}}-2\cdot BC\cdot AB\cdot \cos B \\
& A{{C}^{2}}={{25}^{2}}+{{30}^{2}}-2\left( 25 \right)\left( 30 \right)\cos 80{}^\circ \\
& A{{C}^{2}}=1264.53 \\
& AC\approx 35.6
\end{align}$