Answer:
(a). The shortest length of highway is 79.21 Km.
(b). The angle is 31.0°
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
[tex]h=\sqrt{(40.8)^2+(67.9)^2}[/tex]
[tex]h=79.21\ km[/tex]
(b). We need to calculate the angle
Using formula of angle
[tex]\tan\theta=\dfrac{y}{x}[/tex]
[tex]\theta=\tan^{-1}\dfrac{y}{x}[/tex]
Put the value into the formula
[tex]\theta=\tan^{-1}\dfrac{40.8}{67.9}[/tex]
[tex]\thata=31.0^{\circ}[/tex]
The direction is south of west.
Hence, (a). The shortest length of highway is 79.21 Km.
(b). The angle is 31.0°
