Why are rms values used to calculate power in amplifiers?
Back in the stony ages, before AC, the power into a load was simply the voltage across the load times the current through it, so if an incandescent lamp with 120 volts across it had a current of 1 ampere through it, the heat and light it was generating were equal to what it was receiving from the generator: 120 watts.

Then, when sinusoidal AC came along, with all of its peaks and valleys, 120 volt peaks were no longer able to drive the lamps to full power, but a sine wave with 170 volt peaks could. 

I don't know the genealogy of it, but someone in the mix back then discovered that if one makes a sine table with, say, one degree increments in X and puts 170 volts at 90 degrees, if one took a "sample" by calculating the voltage at every degree and squaring it, added up all the samples, divided that sum by the number of samples taken, and then took the square root of that sum, that Root Mean Square value would cause heating in the load exactly equal to that in the DC case.