Add these vectors algebraically:
A: 350 N @ -50 degrees;

B: 400 N @ 20 degrees S of W;

C: 600 N @ 80 degrees N of W.

The step-by-step approach:

Step 1: Create a data table in which you will list the x- and y- components of each vector and the direction of each, using a positive or negative sign to indicate the direction of the component.  I will place a + and a - sign in each box to remind myself that I must give each component its proper direction.  If I simply make everything positive, I might as well not even do this assignment.  In this case, we have three vectors, so I need a table that has five rows and three columns:

Step 2: Draw an x-y coordinate system and define your directions.  I will call up positive, and to the right positive:

Step 3: Sketch each vector individually (not to scale) and sketch the x- and y- components so you can immediately determine their directions and fill in the proper direction in the data table, even before you fill in the magnitude of each component.

Vector A: Negative 50º is a 4th quadrant vector:

I can now see that the x-component goes to the right (positive) and the y-component goes down (negative).  I fill in those directions in my data table for the A components:

Vector B: 20º S of W is a 3rd quadrant vector:

I see the x-component goes to the left (negative) and the y-component goes down (negative).  I fill in those directions in the table for the B vector:

Vector C: 80º N of W is a 2nd quadrant vector:

I see the x-component goes to the left (negative) and the y-component goes up (positive).  I fill in the table:

Step 4:  Use trigonometry to find the components.  We will use A_x = Acosθ and A_y = Asinθ .  I will then write those values for the x- and y- components in their proper place in the table.

A_x = 350 cos(50) = 225 N

A_y = 350 sin(50) = 268.1 N

B_x = 400 cos(20) = 375.9 N

B_y = 400 sin(20) = 136.8 N

C_x = 600 cos(80) = 104.2 N

C_y = 600 sin(80) = 590.9

Step 5: Add all the x-components to get R_x , the x-component of the Resultant.  Add all the y-components to get R_y , the y-component of the Resultant.

Step 6:  You now have R_x = -255.1 and R_y = +186.  Sketch those components head-to-tail, and draw the Resultant:

Step 7: Use Pythagorean Theorem to find the Resultant: R = √(R_x² + R_y² ) = 315.7.

Step 8: Use inverse tangent to find the angle: θ = tan^-1 (R_y / R_x ) = tan^-1 (186/255.1) = 36.1º.  But this approach only gives me the angle in degrees.  I must now make sure I indicate what quadrant the Resultant is in by adding some notation to indicate where I measured the angle, in this case above the negative x-axis.  I do this by describing the direction of the Resultant as 36.1º, north of west, or N of W.

Step 9:  Make sure you report the full information about the Resultant, including its magnitude and direction. 
The answer here is 315.7 Newtons, @ 36.1º N of W.