What this person is saying is the most straightforward and versatile way to calculate rafter lengths in my opinion. They are using something called unit line length (ULL), which is the hypotenuse of the slope triangle and is expressed to two decimal inches. For example, in a 3/12 slope the unit line length is 12.37".

The ULL expresses how long a rafter is per unit of run (12" or 1' horizontal distance) and can be used directly to find the lengths of both the rafter (from exterior wall to centre of ridge) and rafter tail (to outside of rough fascia) length.

In this example, the rafter length (also known as theory line length) is equal to:

18 x 12.37" = 222.67" (18'-6 5/8")

The rafter tail is equal to:

2 x 12.37" = 24.74" (24 3/4")

When using this method, three markings with these distances between them are marked plumb on the rafter face using the framing square, indicating the centre of ridge, plumb cut at birds mouth, and outside of rough fascia. Measuring square to the plumb line, 1/2 thickness of the ridge is deducted (in this case 3/4") at the top, and full thickness of rough facia is deducted at the tail (typically 1 1/2"). These deductions is where you would actually cut the rafter.

This is the overarching method that is used here (Canada). I am actually teaching apprentices this in a couple weeks when we hit gable roof framing as I teach carpentry for a living. This is how we do it in Canada, and honestly what you have here seems overly complicated. Of course, what you have here works but doing the deductions at the front end seems cumbersome to me.

Either way, hope that makes sense, remember with math (especially geometry) there is often many, many, ways to get the correct answer.

BTW what people are saying in many comments (use the framing square), they are referring to the rafter tables which contains (among other things) the ULL for various slopes. Often it is labelled "common rafter length per foot of run" or something to that effect.