Mass on an accelerated plane

1. The problem statement, all variables and given/known data

There is a mass "m" on an incline plane of mass "M" with angle "θ". At what is the acceleration required of the block to keep the mass from sliding down?

2. Relevant equations

We did this problem using the lagrange approach and got an answer of x"=[mgsinθcosθ]/[M+m(sinθ)^2], but now we are supposed to do it using F=ma, and I can’t get that expression.

3. The attempt at a solution

Setting up the force diagram and using the parallel alternate interior angles thing from geometry, I get that:

cosθ=Fx/mgsinθ so,


But then Fx=(M+m)a, so I get:


Where does the sin^2 come into play?

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