I keep trying to input this into my TI-30xIIB calculator but I keep ending up with a domain error or the wrong answer. The right answer is supposed to be x=41.4. It says to have my calculator in degree mode, which I have put it in and it still doesn't work. Help would be greatly appreciated.

Every calculator is different, but if it is a full scientific calculator that shows you the calculation as you type it in,
(and assuming you mean you want the inverse cos of all the stuff on the RHS)
you would do inv cos ((750*sqrt(2) + 50*sqrt(3)) / 1529)

I've assumed that the /1529 is divide the whole thing, as otherwise you will get an error.