I'm not sure why the system is saying that it can't take the arccos(1.61644771824097) when I plug that in for A) as the answer to phi. I divided the z/p, the argument for the arccos(z/p), which was (9sqrt(3)/2) / (sqrt(93)/2).
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Well, the short answer is that it's saying that because you can't take the arccos(1.61644...). A slightly longer answer is in fact you can't take the arccos of any number bigger than 1 or less than -1, because the domain of arccos is the closed interval [-1,1], because the range of cos is [-1,1].
This information is incredibly important: it means that you made a mistake, in fact at least two mistakes. There is no shame in this, by itself, because everybody makes mistakes. It is critical thought that you should not waste the opportunity to identify and correct the mistakes.
In your case the first instance is that you've miscalculated ρ, it's quite a bit larger than that and simpler. Another mistake is conceptual: you don't have a clear picture of cos(x) and it's relationship with arccos(x). This will hinder in the future you unless you correct it
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