Final answer:
To determine the magnitude of the tension force in member C for equilibrium, we need to draw a free-body diagram and apply the concept of equilibrium. By using Newton's laws and solving the sum of the forces in the y-direction equation, we can find the tension force in member C.
Step-by-step explanation:
The tension force in member C can be determined using the concept of equilibrium. In this mechanical system, the tension force in member C is in balance with the tension forces in the other members. By drawing a free-body diagram and applying Newton's laws, we can solve for the magnitude of the tension force in member C. Let's assume the tension force in member C is Tc. As the system is in equilibrium, the sum of the forces in the y-direction should be zero: T1sin(a1) + T2sin(a2) - Tc = 0, where T1 and T2 are the tensions in the other members, and a1 and a2 are the angles the strings make with the horizontal direction. Rearranging the equation, we find Tc = T1sin(a1) + T2sin(a2).