A highway is to be built between two towns, one of which lies 35.0 km south and 72.0 km west of the other. What is the shortest length of highway that can be built between two towns and what angle would this highway be directed with respect to due west?

If we connect the tips of the distances from the west and south, we form a right triangle with legs equal to 35 km and 72 km. The unknown shortest length is the hypotenuse. Using the Pythagorean theorem, we can say that,

h² = (35 km) ² + (72 km) ²

The value of h is equal to 80.06. Thus, the shortest length of the road that can be built is approximately 80.06 km.