Under the IPC & IRC the maximum length of a fixture arm can be computed by dividing the diameter of the drain by the pitch. If an 1-1/2" line is installed with the code standard 1/4" per foot pitch the maximum lenght would be 1.5 / .25 = 6ft but in this instance the line has a 1/2" pitch so the maximum allowable length would be 1.5 / .5 = 3'. (The bottom of the drain line at the trap weir may not be higher than the top of the line at the vent opening). Both the configurations illustrated above would not pass code for a number of reasons. The simple solution would be to remove the drum trap & extend the length of the tub drain tailpiece. Code will allow up to 24" vertical drop from the tub drain opening to the water level in the trap. Attach a P-trap and run the line with a 1/4" per foot pitch. A wye can be installed on the drain line with the side input angling downstream. You can then put a street 1/8bend on the wye side opening input, which would turn the side opening vertical and attach an AAV where the base of the AAV is 4" above the drain line. REF-IPC 917.4 Location. The air admittance valve shall be located a minimum of 4 inches (102 mm) above the horizontal branch drain or fixture drain being vented The air admittance valve shall be located within the maximum developed length permitted for the vent. The air admittance valve shall be installed a minimum of 6 inches (152 mm) above insulation materials.

actually it looks like I can get everything to line up by adding a 45 elbow between the wall and the trap adapter so the trap adapter is angled towards the sink drain tail instead of pointing straight out

Maybe I have my terminology wrong. I bought a longer waste arm to extend it. Is the coupler the problem? So to make it code, I will have to find a way to access that one compression nut that held the original waste arm pipe? That means I will have to knock out some of my foundation to get to it. I can not believe it passed code the way the original plumber did it. He buried the compression nut that holds the waste arm in brick and mortar. Just a small section is exposed. I can go into the crawl space and cut the waste line where it is glued and start over. I still will have to knock out some of the foundation brick to even get the pipe and nut out but maybe not as much. Thanks for the heads up.

Pressure fittings are defined by the angle of the change in direction they make. I.E. a 90 deg elbow, 45deg elbow, 60deeg elbow etc. In order to help insure we don't mix them, DWV(drain,wste & vent) fittings are defined by the fraction of a circle the change in direction makes. A full circle is 360 degree so a DWV 90 deg elbow would be 360/90 = 4 or properly its called a 1/4 bend. 60deg = 1/6 bend - 45deg = 1/8 bend. A common fitting has a female hub on each end but a "Street fitting" has a female hub on one end and a male raw pipe size on the other end. To make the offset you would begin with a Street 1/8bend with the male pipe end directly into the TEE of the waste & overflow. This would change the direction to 45 degress. Install a length of PVC in the female hub of the 1/8 bend and run the offset down at 45deg to the point where your trap will be. On the bottom end of the 45 deg offset pipe you install another street 1/8 bend with the pipe into the female hub, This will change the direction from 45deg slant to vertically down and it would leave a raw male pipe end that will fit directly into the input of the P-trap. You will find the fittings in both ABS and PVC at any local hardware or home supply store. The choice of which material to use is determined by what kind of pipe you have now. Code prohibits glueing dissimilar plastic so if you have ABS you would use ABS, if you have PVC you would use PVC. In this case you have cast iron so you may use either material as long as all the pieces are the same material.