A ship sails 100mi northeast, then 50mi due south. How far is it from the starting point?

Answer 1

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)