A man starts from his office and goes $8\text{km}$ East. Then he turns to the left and walks for $3\text{km}$. Again he turns left and walks for $8\text{km}$. At what distance is he from the starting point?

Let the starting point be at the origin $(0,0)$.
1. Walking $8\text{km}$ East brings the man to the point $(8,0)$.
2. Turning left (which faces North) and walking $3\text{km}$ brings him to $(8,3)$.
3. Turning left again (which now faces West) and walking $8\text{km}$ changes his x-coordinate back by $-8$, bringing him to $(8-8,3)=(0,3)$.

The distance between the final point $(0,3)$ and the starting point $(0,0)$ is exactly $3\text{km}$.