Thanks a lot for your reply! I am sorry that I was busy last week so no reply to you. I followed you suggestion with following assumptions, θ=85°, w=1, h=1, mg=1, μA=μA,k=0.3 and μB,k=0.5. Following your calculation, I got...
FA=mgw/2[(sinθ-μAcosθ)h-(cosθ+μAsinθ)w]=0.856...