Question 143649
If I read it right, N30 degrees east means 30 degrees east of north.
In that case, first find out how far each boat goes in .5 hr.
boat going east: {{{14* .5 = 7}}}mi
boat going N30E: {{{28*.5 = 14}}}mi
To proceed, you've got to know that a 30:60:90 triangle has sides
that are in the proportion {{{1}}}:{{{sqrt(3)}}}:{{{2}}}. Note that
the sides are opposite their respective angles. So, the boat that
travels 28 mi/hr is at an angle of 60 degrees with east. The 
distance vectors are in the proportion {{{14/7 = 2/1}}} with 60
degrees between them. The distances must be in the proportion
{{{1}}}:{{{sqrt(3)}}}:{{{2}}}, or in this case,
{{{7}}}:{{{7*sqrt(3)}}}:{{{14}}}
So, the distance between them to the nearest tenth is
{{{7*sqrt(3) = 12.1}}}mi