Question

Starting from home, you walk for 1.2 miles in a direction 30 degrees east of north. Then, you turn and walk another 3.1 miles in a direction 20 degrees north of west. At the end of this journey, what is the distance between you and your home?

Answer 1

A=1.2; B=3.1
can you draw it?
for angle between A and B I got 80degress;
then you can use cosine law
\[R^2=A^2+B^2-2AB\cos{\alpha}\]
find R

Answer 2

In this picture, |BO| = R in @bourne13 's solution, and alpha = 20º + 60º. His solution still holds, and is simpler than vector analysis of the three vectors.