As I read it, regan1 has used an infelicitous choice of variable names and used "r" to denote the normal reaction force that is supporting the car against gravity.
When a physicist or mathematician sees "r cos θ" the automatic impulse is to read the "r" as radius, however that does not appear to be the intended reading in this case.
mg > mg cos θ... yes, that's true.
mg cos θ = r... no, that's false.
The correct version is mg = r cos θ
That seems to be the problem; a multiplication where division was called for.