Question 314751
Break up the ship's travel into x and y components.
3 miles at 60=({{{ 3*cos(60)}}},{{{3*sin(60)}}})=({{{1.5}}},{{{2.598}}})
2 miles at 150=({{{2*cos(150)}}},{{{2*sin(150)}}})=({{{-1.732}}},{{{1.0}}})
At this point the ship's position is 
(1.5-1.732,2.598+1.0)=(-0.232,3.598)
In order to return back the ship will have to travel {{{0.232}}} in the x, and {{{-3.598}}} in the y. The total distance is 
{{{D^2=(0.232)^2+(3.598)^2}}}
{{{D=sqrt(13)=3.606}}}
The total distance the ship travels is then,
{{{ Dt=3+2+D=5+sqrt(13)=8.606}}} miles