A plane travels 170 miles at a heading of N 41 degrees W. It then changes direction and travels 165 miles at a heading of N 70 degrees W. How far is the plane from its original position?
Hint: Draw a picture.
You should end up with a triangle with $\displaystyle a = 165\textrm{miles}$ and $\displaystyle b = 170\textrm{miles}$, and the angle between them $\displaystyle C = 151^{\circ}$.
Use the cosine rule to find $\displaystyle c$
$\displaystyle c^2 = a^2 + b^2 - 2bc\cos{C}$.