Question

A highway is to be built between two towns, one of which lies 40.8 km south and 67.9 km west of the other. (a) What is the shortest length of highway that can be built between the two towns, and (b) at what angle would this highway be directed, as a positive angle with respect to due west?

Answer 1

(a). The shortest length of highway is 79.21 Km.

(b). The angle is 31.0°

Step-by-step explanation:

Given that,

The distance in south direction = 40.8 km

The distance in west direction = 67.9 km

(a). We need to calculate the shortest length of highway

Using Pythagorean theorem

`h=√((40.8)^2+(67.9)^2)`

`h=79.21\ km`

(b). We need to calculate the angle

Using formula of angle

`\tan\theta=(y)/(x)`

`\theta=\tan^(-1)(y)/(x)`

Put the value into the formula

`\theta=\tan^(-1)(40.8)/(67.9)`

`\thata=31.0^(\circ)`

The direction is south of west.

Hence, (a). The shortest length of highway is 79.21 Km.

(b). The angle is 31.0°