Question

The three forces shown in the figure below act on a particle (with F1 = 46.0 N, F2 = 59.0 N, θ1 = 61.0°, and θ2 = 29.0°). If the particle is in translational equilibrium, find F3, the magnitude of force 3 and the angle θ3.

Answer 1

The figure is not shown here. But I will try to explain.

The forces are given as,

F1 = 46.0 N,

F2 = 59.0 N,

θ1 = 61.0°,

and θ2 = 29.0°

I think the the first two are in the same quadrant since the angles are less than 90⁰.

F₃cosθ₃ = F₁cosθ + F₂ cosθ₁
=>F₃cosθ₃ = 46cos61⁰ + 59cos29⁰
=>F₃cosθ₃ = 73.90 ----------------(i)
& F₃sinθ₃ = F₁sinθ₁- F₂sinθ₂
=>F₃sinθ₃ = 46sin61⁰ - 59sin29⁰
=>F3sinθ3 = 11.63 --------------(ii)  
=>F3 = [(73.9)² + (11.63)²]
=>F3 = 74.8 Newton
& By (ii)/(i):-
=>θ =tan^-1( 11.63/73.9 )= 8.92