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Ah, such a dilemma, the difficult boss. Legally, there is nothing near a clear answer here as there is significant 'leeway' in how bosses can interact with subordinates. And since his hostility does not appear to involve a sexual nature, it does not necessarily implicate the law on 'hostile work environment' under the law. Also consider if this his his typical behavior or fluke: If a fluke, you may just want to chalk it up to him having a bad day, otherwise, it is an ongoing problem.
However, despite the lack of clear legal ramifications (if any) that is not to say that within your company, there may not be policies covering this behavior (the raising of the voice, does it amount to yelling/screaming, etc.). I have to say it is refreshing to see someone have the nerve, in a respectful manner, to address a boss when he treats us in a way that is inappropriate and which we will not stand for, boss or no boss. (Clearly your boss has emotional issues/mental illness, be it anger management problems, bipolar disorder, what have you.)
The question now is, what are you unwilling, personally and professionally, to let slide (what will you tolerate from him) vs. what are you willing to do, and risk, to stand up for yourself. For instance, I would not hesitate to go to human resources and report the boss' behavior - his losing his cool, his irrationality, his abuse and his creation of an uncomfortable and hostile work environment. It is possible that this boss has been complained about before and eventually there will be a 'straw that breaks the [company's] back'. Another question concerns whether the company would keep the report confidential, but of course, if they don't fire him, he will likely know who reported him. He could certainly make your life miserabe and retaliate, either overtly or in aways that would be difficult to prove. And then, you would almost have to keep reporting his transgressions, to outright protect yourself. There is no guarantee that you wouldn't get fired or that he wouldn't get fired - but the alternative is living with this man on a daily work basis, that could literally cause you such stress and anxiety that you would have to leave anyway. And, if you believe he treats you this way (if it is chronic behavior on his part, vs. a fluke) due to any of the ILLEGAL reasons to treat someone different (ie race, religion, gender, age, etc.), you definitely need to look towards establishing that, as that would clearly violate federal anti-descrimination laws.
Good luck with this. The is extremely common, I am sorry to say, given the volume of mentally ill/disordered people out in the work force, who have difficulty composing themselves for 8 hours a day on the job and maintaining control. (And one of the reasons I became determined, years ago, to work for myself.)
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