Three forces with magnitudes 16 N, 12 N and 21 N are shown in the diagram below. Determine the magnitude of their resultant force and angle with the x-axis

Three forces with magnitudes 16 N, 12 N and 21 N are shown in the diagram below. Determine the magnitude of their resultant force and angle with the x-axis
A. 7.63N,61°
B. 8.71N,61°
C. 7.63N,29°
D. 8.71N,29°

Correct Option: Answer is B

Fx= 12cos32°-16cos26° = -4.20N (right is taken +ve and left is taken -ve)

Fy=12sin32°+16sin26°-21 = -7.63N (up is taken +ve and down is taken -ve)

R2= 4.202+7.632

⇒R2 = 75.86

⇒ R=√75.86

∴R = 8.71 N

tan θ=opp/adj

⇒tan θ= 7.63/4.20

⇒tan θ =1.8095

⇒ θ = tan−1 (1.8095)

θ = 61°
The angle of the resultant force with the x-axis is 61°

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