Question

A highway is to be built between two towns, one of which lies 50.0 km south and 78.0 km west of the other. what is the shortest length of highway that can be built between the two towns, and at what angle would this highway be directed

Answer 1

The shortest length of the highway is 92.64 m and the angle is 32.6°.

Calculation:

The distance is found by Pythagoras theorem,

Distance = $\sqrt{50^{2} +78^{2} }$

               = $\sqrt{2500+6084}$

               = $\sqrt{8584}$

               = 92.64 m

tan(α) = 50/78

tan(α) = 0.64

α = tan⁻ 0.64

α = 32.6°

Hence, the shortest length of the highway is 92.64 m and the angle is 32.6°.

Learn more about calculations of distance and angle here:

https://brainly.com/question/1550786

#SPJ4