Solve Cheese Problem Homework: Find θ1 & θ2

[sheepcountme]

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.

Homework Equations

F=ma
It is suggested we use these: http://i47.tinypic.com/mtxv1z.png

The Attempt at a Solution

I've got the x-axis as T1cosθ1+T2cosθ2=0
and the y-axis as T1sinθ1+T2sinθ2=mg

And now I'm stuck...Please help!

 

[CompuChip]

You are given T1 and T2, right? So you have two equations, which you can use to eliminate θ₂ and solve for θ₁. For this you will probably need the given identities (for example, you will get θ₂ = arccos(... θ₁ ...)

 

[sheepcountme]

Okay, so if I use T1cosθ1+T2cosθ2=0 and plug in the values for T1 and T2 and solve for θ1 I get arccos(1.43cosθ2) and I'm lost again.

Do I set this equal as in: arccos(1.43cosθ2)=arcsin(sqrt((1-arccos(1.43cosθ2))^2)))

and then solve?