physics

The equation you should use is the resolved vector equation for the forces acting on the ring. This equation states that the net force acting on the ring is zero, i.e. the sum of all the forces in the x- and y-directions must be zero. Using the diagram, we can express the equation mathematically: T_1cosθ - T_2sinθ - T_3cosθ + T_3sinθ = 0 Where θ is the angle between the two ropes and the third rope. We can rearrange this equation and solve for T_3 to get: T_3 = (T_1cosθ - T_2sinθ) / (cosθ + sinθ) Once you have the values of T_1 and T_2, you can calculate θ using the lengths of the ropes according to: θ = tan^-1(L_2/L_1) Substituting all the known variables into the equation for T_3 then gives the magnitude of the tension in rope 3, T_3.