A bag of cement of weight Fg hangs from three fires as shown in the figure. Two of the wires make angles theta1 and theta2 with the horizontal. If the system is in equilibrium, show that the tension in the left hand wire is T1 = Fgcos(theta2)/sin(theta1 + theta2)
T1cos(theta1) - T2cos(theta2) = 0
T1sin(theta1) + T2sin(theta2) = Fg (aka T3)
The Attempt at a Solution
Using the equation T1sin(theta1) + T2sin(theta2) = Fg I was able to single out T2 to plug into the other equation (since I'm solving for T1).
T2 = (Fg - T1sin(theta1))/sin(theta2) is what I got
Then I substituted T2 for the equation found into T1cos(theta1) = T2cos(theta2) because the system is at equilibrium in the x direction.
So I get T1cos(theta1) = ((Fg - T1sin(theta1))/sin(theta2)) * cos(theta2)
Simplifies to T1cos(theta1) = (Fgcos(theta2) - T1sin(theta1)cos(theta2))/sin(theta2)
I then divide off cos(theta1) and get the following
T1 = (Fgcos(theta2) - T1sin(theta1)cos(theta2))/(sin(theta2)cos(theta1))
This isn't what I'm supposed to get though. I still have a T1 on both sides of the equation but if I divide it over then it will cancel off.
I'm supposed to be getting Fgcos(theta2)/sin(theta1 + theta2)
and sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
I have all the elements for the denominator on the right side, but two are on top and should be on the bottom.
I obviously messed up big time somewhere, but I'm stuck and don't know where to go from here.