Something about physics

Few days ago, my friend asked me a question related to normal force:
Is it R cos Ө = mg or mg cos Ө = R
I'll post a picture here


After thinking and asking here and there, I have come to an understanding that it is mg cos Ө = R

Here is my explanation. Tell me if I am wrong.

when no other external forces are acted upon the object, R can only be less than or equal to mg, but not greater than mg. Am I correct?
Therefore when considering the equation
RcosӨ = mg
cosӨ = mg/R
since that mg>R, mg/R > 1
cosӨ = 1 would be impossible
Therefore this equation is wrong.
However when considering the equation
mg cosӨ = R
cosӨ = R/mg
since that mg>R, R/mg < 1
cosӨ < 1
Therefore this equation can be used.

However, under different situation where R is not dependent only on mg, the equation might be different.