Question

The resultant of two forces in a plane is 400 N at 120 degrees. If one of the forces is 200 lbs at 20 degrees what is the other force?

Answer 1

Given:

$R=400\:\rm N$

$\theta=120^{\circ}$

$F_1=200\:\rm lbs=890\: N$

$\alpha=20^{\circ}$

The resultant force

$$\bf R=F_1+F_2$$

Hence,

$$\bf F_2=R-F_1$$

$$F_2=\sqrt{R^2+F_1^2-2RF_1\cos(120^{\circ}-20^{\circ})}$$

$$F_2=\sqrt{400^2+890^2-2*400*890\cos(100^{\circ})}\\ F_2=1037\:\rm N$$