Answer
The distance between the ships after two hours is about 77 miles.
Work Step by Step
First, one must find how far the ships are from the port. The one that is going northeast has traveled $20\frac{mi}{h}\cdot 2h=40$ miles. The other one has traveled $28\frac{mi}{h}\cdot 2h=56$ miles. After finding the angle between the routes of the ships, which is $180º-32º-42º=106º$, sufficient data is found to find the distance between them using the law of cosine.
$d^2=40^2+56^2-2(40)(56)\cdot $cos$(106º)$
$d^2=1600+3136-4480\cdot (-0.28)$
$d^2=4736+1235$
$d=\sqrt{5971}\approx 77$ miles
