Answer:
 F = 233.52 N,  θ' = 351.41º
Explanation:
In this exercise we must find the net force applied on the donkey.
For this we use Newton's second law, where we create a reference frame with the horizontal x axis
let's decompose the forces
Jack
         = 80.5 N
Jill
        cos 45 = F_{2x} / F₂2
        sin 45 = F_{2y} / F₂2
        F_{2x} = F₂ cos 45
        F_{2y} = F₂ sin 45
        F_{2x} = 81.7 cos 45 = 57.77 N
        F_{2y} = 81.7 sin 45 = 57.77 N
Jane
       cos (270 + 45) = F_{3x} / F₃3
       sin 315 = F_{3y} / F₃
       F_{3x} = 131 cos 315 = 92.63 N
       F_{3y} = 131 sin 315 = -92.63 N
the force can be found in each axis
X axis
          F_{x} = F_{1x} + F_{2x} + F_{3x}
          F_{x} = 80.5 +57.77 + 92.63
          F_{x} = 230.9 N
Axis y
          F_{y} = F_{1y} + F_{2y} + F_{3y}
          F_{y} = 0 + 57.77 -92.63
          F_{y} = -34.86 N
we can give the result in two ways
a) F = (230.9 i ^ - 34.86 j ^) N
b) in the form of module and angle
we use the Pythagorean theorem
          F = √(Fₓ² + F_{y}²
         F = √(230.9² + 34.86²)
         F = 233.52 N
let's use trigonometry for the angle
         tan θ = 
         θ = tan⁻¹ (\frac{F_y}{F_x} })
         θ = tan⁻¹ (-34.86 / 230.9)
         θ = -8.59º
if we measure this angle from the positive side of the x-axis counterclockwise
           θ' = 360 -θ
           θ‘= 360- 8.59
           θ' = 351.41º