Answer
$61.7\ mi$.
Work Step by Step
Step 1. Draw a diagram as shown in the figure. The first ship traveled from point C, $3(14)=42\ mi$, to point A. The second ship traveled from C, $3(10)=30\ mi$, to point B. The angles are given from the bearings.
Step 2. In triangle ABC, we have the angle
$C=12^\circ+90^\circ+(90^\circ-75^\circ)=117^\circ$.
Step 3. Use the Law of Cosines. Letting $AB=c$, we have $c^2=42^2+30^2-2(42)(30)cos(117^\circ)\approx3808$, which gives $c\approx61.7\ mi$. That is, the two ships are about 61.7 miles apart after 3 hours.
