Nowhere in your literature do I find the length of the cable for tethered DT throttles.
The length is not published because there are variations between each order supplied to us by our vendor.
Before the "coily" cords, the cable length was 7 feet.
Checking my own DT400 throttle, the coiled cable is 31 inches long "at rest" and 84 inches at its maximum extension.
However, it is quite likely that you will have a cable which might be slightly different.
The DT400R will have a very short cable, long enough to connect to LocoNet to call up or release locomotives.
It is a mistaken assumption that the cord is the radio antenna, the antenna is actually inside the DT400R.
The UT Utility Throttles will have similar cords.