Find the angles in a tension on 2 ropes problem

[bkhurley]

Homework Statement

A 4.50 kg block of gruyere cheese is suspended as shown. Rope 1 on the left has a tension of 28.3 N; rope 2 on the right has a tension of 40.5 N.
(a) What is θ1, the angle made by rope 1? (b) What is θ2? State each angle as the positive angle "inside" the triangle the ropes form.
http://i47.tinypic.com/ivy260.png

Homework Equations

Newton's second law
The problem also included these identities:
http://i47.tinypic.com/mtxv1z.png

The Attempt at a Solution

I tried to solve for one of the thetas using the equation for the x-axis
T1cosθ1+T2cosθ2 = 0

and then substitute it in the equation for the y-axis *trying* to use the trig identities
T1sinθ1+T2sinθ2 = mg

I doubt I'm doing it right but either way I'm way stuck after an hour
help!please!

 

[rock.freak667]

The Attempt at a Solution

I tried to solve for one of the thetas using the equation for the x-axis
T1cosθ1+T2cosθ2 = 0

and then substitute it in the equation for the y-axis *trying* to use the trig identities
T1sinθ1+T2sinθ2 = mg

I doubt I'm doing it right but either way I'm way stuck after an hour
help!please!

this one should be T₁cosθ₁-T₂cosθ₂ = 0

yes you are going correct, just take the equation I corrected for you and isolate either T₁ or T₂ and substitute into the next equation.

 

[bkhurley]

okay sounds good but I'm not solving for T I'm solving for both thetas