physics
posted by kj .
The three forces shown in the figure below act on a particle (with F1 = 48.0 N, F2 = 58.0 N, θ1 = 63.0°, and θ2 = 27.0°). If the particle is in translational equilibrium, find F3, the magnitude of force 3 and the angle θ3.
F3 = 1 N
θ3 = 2° (counterclockwise from the +xaxis)

Is that your answer? If so, it is wrong. How did you get it? It looks like very a wild guess.
There is no way a 1 N force can balance F1 and F2, which are much larger and in both in the first quadrant. F3 is what is called the equilibrant force. It must be in the third quadrant to balance the other 2 forces.
The way to solve this problem is set the sum of the x components of F1, F2, and F3 equal to zero, and to the same with the y components. That will allow you to solve for F3,x and F3,y.