Answer:
[tex]\theta=287^o[/tex]
Step-by-step explanation:
Position in the Plane
If we place an object in a plane and mesure its x and y coordinates, we are referencig its position according to the rectangular system. Other popular way to reference positions is in polar form or magnitude-angle form. If we have the rectangular coordinates (x,y), we can easily find the polar coordinates [tex](r,\theta)[/tex] (and vice-versa). We use the formulas
[tex]r=\sqrt{x^2+y^2}[/tex]
[tex]\displaystyle tan\theta=\frac{y}{x}[/tex]
We have x=31.4 Km East (a positive coordinate) and y=-102.5 Km South (negative because it's pointing downwards). we need to find the angle respect to the East reference where [tex]\theta=0^o[/tex]. Check the image below for reference.
[tex]\displaystyle tan\theta=\frac{-102.5}{31.4}=-3.264[/tex]
[tex]\theta=-73^o[/tex]
The angle can be also given as a positive quantity by adding 360^o
[tex]\theta=-73^o+360^o[/tex]
[tex]\boxed{\theta=287^o}[/tex]
