physics question

Question

A ship sails 30 kilometers 70 degrees north of east. It then turns 110 degrees to the west, giving it a new heading of 0 degrees north of west.
After sailing another 30 kilometers, how far is the boat (in kilometers) from where it started?

Answer 1

This is a vector addition problem.   The tail to head construction gives an isosceles triangle with vertex angle = 70 degrees and sides of length 30 km.  The law of cosines gives the length, L,  of the resultant vector as :

 

L² =  30² + 30² - 2 30 30 cos(70).   This works out to L =  34.4