# Why can't I get the vector answer shown?

Vectors in geometry

### Why can't I get the vector answer shown?

In the attached pic, I don't know how the answer for A + B + C + D has a magnitude of 29 and a direction of 157° from x (or 23° N of W)
My solution shown below:

Choosing up and to the right as positive directions, and rounding to two decimal places:
Ax = +15cos60°=7.5
Ay = +15sin60°=12.99
Bx = 10
By = 0
Cx = 0
Cy = -25
Dx = -50cos28°= -44.15
Dy = -50sin28°= -23.47

Sum in x-direction: -26.65
Sum in y-direction: -35.48
|R|=$$\sqrt{(-26.65)^2+(-35.48)^2}$$ = 44.37
\theta = tan^(-1)=(-35.48/-26.65) = 53.09° South of West

But the answer provided is |R| = 29 and /theta = 23° N of W
Can anyone help?
Attachments Vector Addition Problems.PNG (14.01 KiB) Viewed 128 times
Guest

### Re: Why can't I get the vector answer shown?

OP here. Please see the attached for my answers for all 3 vector additions.
Attachments Vector Addition My Answers.PNG (71.42 KiB) Viewed 123 times
Guest

### Re: Why can't I get the vector answer shown?

OP here again. Small typo on the last direction. Should say 59° S of W, not S of E.
Guest