A ship sails 100mi northeast, then 50mi due south. How far is it from the starting point?
break the first leg into a N,and an E part.
Npart=100*.707=70.7mi
Epart=100*.707=70.7 mi
now go 50 mi S
resultant:
Npart=20.7N
Epart=70.7E
distance=sqrt(Npart^2 + Epart^2)