Statics problem -- Rectangular plate lying on two inclined surfaces

[Mzaa]

Homework Statement

https://www.img.in.th/image/VNaqVa
https://www.img.in.th/image/VNa3k9

This is my home work.

Homework Equations

The Attempt at a Solution

I have a problem with the force at A and B. I don't know how to use N_A N_B in the term of α and β to use moment calculation. I got that In x-axis N_Asin∝=N_Bsinβ, but in the y-axis it still confuse.

 

[haruspex]

Homework Statement

https://www.img.in.th/image/VNaqVa
https://www.img.in.th/image/VNa3k9
This is my home work.

Homework Equations

The Attempt at a Solution

I have a problem with the force at A and B. I don't know how to use N_A N_B in the term of α and β to use moment calculation. I got that In x-axis N_Asinα=N_Bsinβ, but in the y-axis it still confuse.

How many forces act on the plate?
With that many forces acting on a body in equilibrium, what can you say about the lines of action of the forces?

 

[Mzaa]

I recently searched for definition of "line of action of force",but I still confuse.Are they the line passing through A and B and they're pararelled?

 

[haruspex]

Are they the line passing through A and B

Yes. The normal force at A passes through point A. This is important for finding the torque that a force exerts about a given axis.
Here you have three forces acting on the plate. The lines of action of the two normal forces intersect at some point, P. If we take moments about that point, what torque do those two forces exert about P?
The third force is gravity.
If the system is in equilibrium, what does that tell you about the torque the gravitational force exerts about P?