# Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in the figure. The sum of the forces F_A and F_B exerted on the unit by the horizontal cables is parallel to the line L, and F_A=4200 N. Determine F_B? Determine the magnitude of F_A+F_B?

Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in the figure. The sum of the forces ${F}_{A}$ and ${F}_{B}$ exerted on the unit by the horizontal cables is parallel to the line L, and ${F}_{A}=4200$ N. Determine ${F}_{B}$? Determine the magnitude of ${F}_{A}+{F}_{B}$?
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l1koV
sum of forces is along line L
so they must be balancing in horizontal components
${F}_{b}\mathrm{sin}\left(30\right)={F}_{a}\mathrm{sin}\left(50\right)$
${F}_{b}\mathrm{sin}\left(30\right)=4200\mathrm{sin}\left(50\right)$

net force ${F}_{a}+{F}_{b}={F}_{a}\mathrm{cos}\left(50\right)+{F}_{b}\mathrm{cos}\left(30\right)$
$=4200\mathrm{cos}\left(50\right)+6434.7733222\mathrm{cos}\left(30\right)$
$=8272.3851253$ N