Answer
23.1 mi
Work Step by Step
Step 1. Identify the given quantities: angle $\theta=65^{\circ}$, start time 2pm, end time 2:30pm, speed1 50 mi/h, speed2 30 mi/h
Step 2. Time of travel 0.5 h, construct the triangle, side 1 $0.5\times50=25mi$, side 2 $0.5\times30=15mi$, angle in between $\theta=65^{\circ}$
Step 3. Use the Law of Cosines, the distance between the two cars $d^2=25^2+15^2-2\times15\times25cos65^{\circ}$ which gives $d\approx23.1mi$
