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Resultant of concurrent forces: Direction angle θ of the resultant with the horizontal. Context: Several forces act at a point with components ΣF<sub>x</sub> (horizontal) and ΣF<sub>y</sub> (vertical). Choose the correct relation for the inclination θ of the resultant.

Difficulty: Easy

tanθ = ΣF_y / ΣF_x
tanθ = ΣF_x / ΣF_y
tanθ = (ΣF_x + ΣF_y) / (ΣF_x − ΣF_y)
tanθ = (ΣF_x · ΣF_y)

Correct Answer: tanθ = ΣF_y / ΣF_x

Explanation:

Given/Definitions

Resultant vector R has components R_x = ΣF_x, R_y = ΣF_y.

Derivation
tanθ = (opposite)/(adjacent) = R_y / R_x = ΣF_y / ΣF_x.

Verification/Notes
When ΣF_x = 0, the resultant is vertical (θ = 90°). Sign conventions determine quadrant but not the basic ratio.

Final Answer
tanθ = ΣF_y / ΣF_x

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