Find tension in angled cables holding steel plate

[megr_ftw]

Homework Statement

I found that the steel plate weighs 23.1 kN from using the volume and density of steel. The length of L1=3.2m, L2= 3.9m. The angle on the left, theta, equals 94.4 degrees and alpha equals 54.9 degrees. I am just confused on how to find the tension in the cables. If someone could point me in the right direction. I have to find stress and bearing stress but I can easily do that, the tensions are just confusing to me

Here is a diagram:

Homework Equations

F=mg

The Attempt at a Solution

I found the weight of the steel plate from the volume and density of steel (in statement). I am sure this is simple, but the 94.4 degrees is what's weird to me since I'm use to dealing with right triangles...

 

[Q_Goest]

Hi megr. The tension in the cable can be broken down into a verticle and horizontal component. Just sum the forces in the verticle direction and horizontal direction as you would for any static equilibrium problem and you should be able to deduce the tension in the cables.

 

[megr_ftw]

I know that part, but how? the angle on the left is 94.4 degrees and doesn't form a right triangle. I can't just use T_1*cos(94.4) since that won't work. I am so frustrated with the problem and how to find any of the components for just one cable

 

[Q_Goest]

cos(94.4/2) = Fy/T
where Fy = verticle componenet of force
T = Tension in cable.

 

[nvn]

megr_ftw: Hint: Use the given geometry, including the dimensions given on the plate, to figure out beta1 or beta2. In other words, initially, it is a slightly involved geometry problem, but can be figured out using the given geometry and dimensions, using trigonometry. We are not allowed to give you the relevant equations nor work out the trigonometry for you. If you show your work, we could check your math.