For the sake or convention, I'll do all the calculation using the 16.97 (17) run for hip and valley rafters.

Knowing that hips and valleys are the diagonal projections of the hypotenuse of an isosceles right triangle there are a few Methods that you can employ to calculate their length.

Method 1:

1. You can simply multiple 192" (s) by 1.4142 to get the hip of valley rafter run, in this case would be 271-17/32"
2. Using the Pythagorean Theorem . . .c² = a² + b² for both a and b you get,
3. (square root)hrl = (271.53² + 128²)
   
   the roof rise doesn't change for a hip or valley just it's run changes.
   
   
4. So, (square root)hrl = (73728.54 + 16384) or (square root)hrl = (90112.54) and finally the
5. hrl/vrl = 300.1875 (300-3/16")

This is the unadjusted hip or valley rafter length.

You now can once again determine the ir for the hip rafter. ir = (128 * 12) / 300.1875
ir = 5.12 (5-1/8") Now set your square to this number a cut the hips.

Method 2:

1. Using the Pythagorean Theorem . . .c² = a² + b² for both a and b once again, but with a slight twist. You get this. . .

2. (square root)hrl = ((r² )*2) + (rz²) =
3. (square root)hrl = ((192² )*2) + 128²) =
4. (square root)hrl = (73728) + (16384)
5. (square root)hrl = (90112) or

6. hrl/vrl = 300.1875 or 300-3/16".

   This is the unadjusted hip or valley rafter length once again.