Serway & Jewett — The Laws of Motion: Problem 18

A bag of cement whose weight is \(F_g\) hangs in equilibrium from three wires as shown in Figure P5.18. Two of the wires make angles \(\theta_1\) and \(\theta_2\) with the horizontal. Assuming the system is in equilibrium, show that the tension in the left-hand wire is \(T_1 = \frac{F_g \cos \theta_2}{\sin(\theta_1 + \theta_2)}\).