Vectors (Direction of Resultant Displacement)

[Heat]

Homework Statement

A disoriented car drives a distance 3.05 km north, then a distance 4.55km west, and then a distance 1.40 km south.

Find the magnitude of the resultant displacement, using the method of components.

Find the direction of the resultant displacement (in West of North degrees), using the method of components.

The Attempt at a Solution

I managed to find the magnitude of the resultant displacement to be 4.84.

This is because:

x y
A 3.05 0 3.05
B 4.55 -4.55 0
C 1.40 0 -1.40
________________________
-4.55 1.65
Resultant Displacement = 4.84

Now for the direction is what I am having conflicts with,
I did the following:

arctan (1.65/-4.55) = -19.9

I would assume that the following degree is the angle between the resultant displament and the x axis, leading it to be 19.9 degrees. I got it wrong.

Then I would assume it would be 180-19.9, which is 160.1. This is wrong also.

I would then assume in my last try that it would be 90-19.9.
It would turn out to be 70.1.

But why would it be the inner angle between the resultant displacement and the y-axis and not between the x axis?

 

[Dick]

Because they asked for "West of North degrees". North is the y axis.

 

[Heat]

So what would they have to say for it to be 19.9?

North of West Degrees...

 

[Dick]

Exxxxactly.