Question

A woman leaves home and walks 5miles west, then 2 miles southwest. How far from home is she, and in what direction must she walk to head directly home? Round to 2 decimal places.

Answer 1

Using the Pythagorean theorem, we can determine that the woman is 5.39 miles away from home.

To determine the direction she must walk to head directly home, we can draw a compass rose and label the directions. She started by walking west (which is 270 degrees on the compass), and then she turned southwest (which is 225 degrees on the compass). The direction she needs to walk to head directly home would be the opposite direction of the vector connecting her current location to her starting point. This vector has a direction of 45 degrees on the compass (i.e. the direction north of northeast).

So, the woman needs to walk in the direction of 045 on the compass to head directly home.