A chandelier with mass m is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension T1 and makes an angle of θ1 with the ceiling. Cable 2 has tension T2 and makes an angle of θ2 with the ceiling.
Find an expression for T1, the tension in cable 1, that does not depend on T2.
Express your answer in terms of some or all of the variables m, θ1, and θ2, as well as the magnitude of the acceleration due to gravity g.
The Attempt at a Solution
So far I have found the x and y components:
ΣFx = 0 = -T1cosθ1 + T2cosθ2
ΣFy = 0 = T1sinθ1 + T2sinθ2 - mg
Now I need to eliminate T2 from this pair of equations and solve for T1, but I can't figure out how to do this.