Final answer:
The last component of assessment by an EMT for a stable trauma patient with shoulder pain is likely to be the baseline vitals, which provide a reference for the patient's normal physiological state.
Step-by-step explanation:
The last component of assessment that the EMT would ascertain in completing a secondary assessment on a stable trauma patient with shoulder pain after playing football would likely be baseline vitals. Breath sounds and history would have been assessed earlier in the patient evaluation; the physical exam is typically conducted before checking vitals to ensure that no immediate life-threatening conditions are overlooked. Checking baseline vitals allows the EMT to establish a reference point for the patient's normal physiological state, which can be instrumental for further diagnosis and treatment.