Simple question on Conservation of Momentum in 2 directions

[mcapuchin]

Homework Statement

A firework at rest with a mass of 0.90kg explodes into 3 pieces. One piece has a mass of 0.25kg and moves horizontally at 36m/s [N]. Another has a mas of 0.35kg and moves horizontally at 32m/s [S50°W]
Find the velocity of the third peice[/B]

Homework Equations

SOH CAH TOA
Conservation of Momentum
Pythagorean Theorem

The Attempt at a Solution

Let N and E be positive[/B]
I first split up both the x and y components
v_1y=36m/s
v_1x=0m/s
v_2y-32cos50=-20.57m/s
v_2x=-32sin50=-24.51m/s

Now I subtracted the 2 masses from .90kg which gave me a mass of .30kg.
Then I used the conservation of momentum for both the x and y components, which must equal zero as the object was at rest initially
PT=0
0=m₁v_1fx-m₂v_2fx+m₃v_3fx
0=(0.25kg)(0m/s)-(0.35kg)(24.51m/s)+(0.30kg)v_3fx
v_3fx=28.59m/s

0=m₁v_1fy-m₂v_2fy+m₃v_3fy
0=(0.25)(36m/s)-(0.35)(20.57m/s)+(0.30kg)v_3fy
v_3fy=6.0m/s

To find the final velocity with the x and y components
a²+b²=c²
6²+28.59²=820
√820=28.63
v_3f=28.63m/s

Now we find the angle of the magnitude
tan^-1=(6/28.59)
=11.85°

However, this is where I'm stuck. How do I know if it is north or south or west or east? I looked at the book and my calculations are correct, but they say it is S11.9W. How do I determine this?

 

[jedishrfu]

Try drawing a diagram of the event and trajectories and see if things make sense from it.

 

[mcapuchin]

Thanks for the suggestion, I think there's a typo in the text as on the diagram I drew it makes sense that it will be E11.85S. Will point it out to my teacher.