Solving for Tension in Cement Bag Wires

[intriqet]

Homework Statement

A bag of cement of weight 350 N hangs from three wires as suggested in the figure below. Two of the wires make angles θ1 = 50.0° and θ2 = 27.0° with the horizontal. Assuming the system is in equilibrium, find the tensions in the wires.

Homework Equations

Newton's Laws of motion

The Attempt at a Solution

I know that the tension for T3 is just equal to the weight. But how do I split the force between the remaining two strings?

 

[rl.bhat]

Find the vertical and horizontal components of T1 and T2.
In equilibrium condition, Vertical components add up to ...?
What happens to horizontal components?
Solve these two equations to find T1 and T2.

 

[intriqet]

Please pardon my stupidity. How would I break up T1 and T2 into components? My first impulse was to do 350costheta and 350sintheta for each tension force and its respective theta but that's obviously not the way to go.

I also figured that if the system was in equilibrium. F1total + F2total + F3total = 0, but I have no idea where to go from there because I still have 2 unknowns and only 1 equation

 

[rl.bhat]

The vertical components are T1*sinθ1 and Τ1*sinθ2 Their sum is equal to 350 N.
Horizontal components are T1*cosθ1 and Τ1*cosθ2 and they are equal. As I have told you, you have two equations. Solve them to find T1 and T2.