Answer:
[tex]F_r \approx 978.3N[/tex]
[tex]\theta =44 \textdegree[/tex]
Explanation:
From the question we are told that
Connie pulls with a force of [tex]F_c=200 N[/tex]
At an angle [tex]\theta _c=20 \textdegree[/tex]
Randolph pulls with a force of [tex]F_R=800 N[/tex]
At an angle [tex]\theta _R=50 \textdegree[/tex]
Generally the horizontal axis can mathematically be represented as
[tex]f_x=f_ccos\theta _c+F_Rcos\theta _R[/tex]
[tex]f_x=200*cos20+800*cos50[/tex]
[tex]f_x=702.2N[/tex]
Generally the vertical axis can mathematically be represented as
[tex]f_y=f_csin\theta _c+F_Rsin\theta _R[/tex]
[tex]f_y=200*sin20+800*sin50[/tex]
[tex]f_y=681.24N[/tex]
Generally the resultant force [tex]F_r[/tex] is mathematically given by
[tex]F_r=\sqrt{f_x^2+f_y^2}[/tex]
[tex]F_r=\sqrt{702.1686119^2+681.2395832^2}[/tex]
[tex]F_r=978.3230731N[/tex]
[tex]F_r \approx 978.3N[/tex]
Generally the Direction [tex]\theta[/tex] of force is mathematically given by
[tex]\theta =tan^-^1(\frac{f_c}{f_y})[/tex]
[tex]\theta =tan^-^1(\frac{681.23}{702.16})[/tex]
[tex]\theta =44 \textdegree[/tex]
