The angle θ is approximately 58.7 degrees.
To determine the angle θ in a system where two cables are supporting a 82.0 kg mass, we can consider the forces acting on the mass. Each cable exerts a tension force on the mass, and these forces can be decomposed into horizontal and vertical components. The vertical components of the tension forces, when added together, must balance the gravitational force acting on the mass.
Given that the tension in each cable is 471 N, the vertical components of these tensions can be determined using trigonometric relationships. Considering the forces in the vertical direction, the sum of the vertical components of tension forces equals the gravitational force (mass times gravitational acceleration). By solving for the angle θ using trigonometric functions, the angle is found to be approximately 58.7 degrees. This calculation ensures equilibrium in the vertical direction and provides the angle at which the cables support the given mass.