Resolving vectors

1) Taking forces about the x - axis:
(4 cos 30 - 6 cos 30) + (10 cos 30 - 12 cos 30) = - 3.4641 N giving the horizontal component for resultant force, R N.

2) For the y - axis:
(4 sin 30 + 6 sin 30) - (12 sin 30 + 10 sin 30) => 5 N - 11 N = - 6 N
vertical component of resultant, R N.

3) Combining the 2 components to obtain the final resultant in a particular direction:
R N = root (- 3.46² + - 6²) = root (11.97 + 36) = root 47.97 = 6.926 N resultant vector.

4) To find its angle from the horizontal:
Tan x^o = (- 6 / - 3.49) = 1.7192
Tan ^-1 1.7192 = 59.81^o rounded to 60^o.
x = 180^o - 60^o = - 120^o going clockwise from point (0, 1) in a negative direction from the horizontal.

The final resultant vector of 6.93 N at - 120^o.