## Precalculus (6th Edition) Blitzer

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