Vectors & Forces: Find Resultant Direction & Magnitude

[themadhatter1]

Homework Statement

If θ=30 degrees find the direction and magnitude of the resultant of these forces.
[PLAIN]http://img194.imageshack.us/img194/7899/image2iw.jpg

Homework Equations

The Attempt at a Solution

Ok, so I know I have to add both of the vectors. I need to find the coordinates to do so. The first vector's coordinates must be <220,0>. Next I need to find the second vector's coordinates:

x=150cos30
x=[150√(3)]/2
y=150cos30
y=75

so the second vector has the coordinates <[150√(3)]/2,75>

If you add the second and the first vectors you get <[590√(3)]/2,75>

Then I found the magnitude of this new vector to be 590.63 Newtons. However, this is wrong because the book's answer section says the magnitude should be 357.85 Newtons.

If i go on to find the direction that also turns out wrong. What am I doing wrong?

 

[Mark44]

The x-component of your vector sum is 590*sqrt(3)/2, which is about 510. That is incorrect, and is too large (you should get about 350). Take a look again at your calculation for this component.

 

[themadhatter1]

Ahh. Thanks, I found my error. The x component should be:

[440+150√(3)]/2