Applied Mechanics and Graphic Statics
The resultant of two forces ‘P’ and ‘Q’ acting at an angle ‘θ’, is

P² + Q² + 2PQ cos θ
P² + Q² + 2PQ tan θ
P² + Q² + 2P sin θ
√(P² + Q² + 2PQ cos θ)

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Applied Mechanics and Graphic Statics
If a set of given forces are such that their free vectors build a closed polygon, then

The resultant force is zero but resultant couple is not zero
The resultant force and resultant couple are always zero
The resultant force is zero but resultant couple may not be zero
The resultant force and resultant couple both may not be zero

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