Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 17.0 m, B = 10.0 m, C = 11.0 m, and D = 23.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the direction as a positive (counterclockwise) angle from the +x axis.

Answer 1

This cannot be commented on without knowing the directions of each vector.

Here is my suggestion. Add all the x components MEASURED FROM THE X AXIS COUNTER CLOCKWISE:
Rx=A*cosTheta+B*cosTheta+....+E*cosTheta

Ry=A*sinTheta+B*sinTheta+...+EsinTheta.

Now for magnitude:
R=sqrt(Rx^2 + Ry^2)

Angle=arcTan(Ry/Rx). Remember that is the principle angle, there is at least one other angle in the other quadrants that will work. Take a look at the vectors,especially if either Rx or Ry are negative