Answer:
the angle between the forces is 36°
Step-by-step explanation:
if we assign the x axis to F1=595 N , thus F2=497 has an angle α respect with the x axis such that
F total x = F1 + F2 cos α
F total y = F2 sin α
and since
F total² = (F total x)² + (F total y)² = (F1 + F2 cos α)²+(F2 sin α)²
F total² = F1² + 2*F1*F2cos α + F2² cos² α + F2² sin² α
F total² = F1² + 2*F1*F2cos α + F2²
therefore
cos α = [F total² - (F1²+F2²)] /(2*F1*F2)
replacing values
cos α = [F total² - (F1²+F2²)] /(2*F1*F2) = [1039² - (595²+497²)]/(2*595*497)
cos α = 0.809
α = cos⁻¹ 0.809 = 36°