Easy addition of polar vectors?

[byoung]

I'm trying to add polar vectors, which is easily accomplished on the 50g or 48 series using cylindrical or spherical mode. Specifically, I'm learning the Prime by duplicating example 3 on page 178 of the HP48SX manual. In this example, we want to add three vectors (I'll use "<" to represent the angle symbol):

[170 <143] + [185 <62] + [100 <-99] = [178.937 <111.149]

This resultant is then resolved along the 175 degree line by taking the dot product with [1 <175] to get 78.86.

I can achieve the first part using a ridiculous number of conversions with the rectangular_coordinates() and polar_coordinates() commands. The last part is even worse because I have to convert the resultant and the [1 <175] vector back to rectangular coordinates and the copy and paste both of these into the dot() command.

This seems much more complicated than it should be to do a routine, basic engineering calculation. Am I missing something obvious? Also, I can only do this in CAS. I'd prefer RPN, but this seems out of the question.

Thanks.