Answer:293.45 N ,
[tex]\theta =47.38^{\circ}[/tex]
Explanation:
Given
Three force of magnitude 360 N, 200 N, 360 N at an angle of [tex]-30^{\circ}, [/tex][tex]45^{\circ}, 135^{\circ}[/tex] w.r.t to x axis.
Resolving forces in x and y direction
[tex]R_x=360cos30+200cos45+360cos135=198.605 N[/tex]
[tex]R_y=360sin(-30)+200sin(45)+360sin(135)=216.04 N[/tex]
Net Force replace these three force is
[tex]R_{net}=\sqrt{(R_x)^2+(R_y)^2}[/tex]
[tex]R_{net}=\sqrt{198.605^2+216.04^2}=293.45[/tex]
For direction
[tex]tan\theta =\frac{R_y}{R_x}=\frac{216.04}{198.605}=1.087 [/tex]
[tex]\theta =47.38^{\circ}[/tex] w.r.t to x axis
