Solving for Tension in a Suspended 28kg Sign

[chrisfnet]

Homework Statement

Attached is a diagram of the problem.

A 28kg sign is suspended by two massless cables. Find the tension in each.

Homework Equations

The Attempt at a Solution

I'll call the cable at 57 degrees T₁ and the other cable T₂.

T₁∙cos 57 + T₂∙cos 36 = 9.8m/s²∙28kg
T₁∙cos 57 + T₂∙cos 36 = 274.4N

T₁∙sin 57 + T₂∙sin 36 = 0N

This is where I'm getting confused - rusty on my algebra with simultaneous equations. Am I on track so far though, then just solve for T₁ and T₂?

 

[chrisfnet]

T₁ = (-T₂∙sin 36)/sin 57

Substitute that into the first equation...

(-T₂∙sin 36∙cos 57)/sin 57 + T₂∙cos 36 = 274.4N
T₂ = 143.05N

Then solve for T₁.

T₁∙cos 57 + (143.05N)∙cos 36 = 274.4N
T₁ = 291.33N

 

[rl.bhat]

From third equation you can write
T1 = - T2*sin36/sin57.
Substitute this value in eq. 2 and solve for T2.

 

[chrisfnet]

From third equation you can write
T1 = - T2*sin36/sin57.
Substitute this value in eq. 2 and solve for T2.

Thanks - that's exactly what I ended up doing. Not sure why I was over-complicating it. Could anyone confirm my solutions are correct?

Thanks!

 

[chrisfnet]

Can anyone verify that my work is correct? Thanks!