Determine Fb and the magnitude of Fa + Fb.?

[Marley]

Two snowcats tow a housing unit to a new location in Alaska. The sum of the forces of Fa and Fb exerted on the unit by the horizontal cables is parallel to the line L, and Fa=4500N. (between Fa and line L it's 50deg, and between Fb and line L it's 30deg)

[getfreducated]

If the lateral motion is zero, then...

4500sin(50) = Fb* sin(30) which gives you everything for which you asked.

-F

EDIT: After the heavy lifting was done, I see PINKGREEN (Lilly Pulitzer??) was nice enough to plug and chug for us, but the answer can only be quoted to two sig. figs. NOT to within a Newton, but he certainly pressed the right keys on the calculator!!

[PINKGREEN]

Since the resultant force R,Fa & Fb form a closed
triangle,then
Fb/sin50*=Fa/sin30*=>
Fb=4500sin50*/sin30*=>
Fb=6894N (correct to a newton)

R/sin(180-30-50)*=4500/sin30*=>
R=8863N (correct to a newton)