Which of the following is the correct therapy for a hypotensive patient with third degree heart block and a pulse of 38 beats per minute?

The most appropriate therapy for a hypotensive patient with third-degree heart block and a heart rate of 38 beats per minute is transcutaneous pacing. In the context of third-degree heart block, also known as complete heart block, there is a disconnection between the atrial and ventricular activity, leading to a very slow heart rate and inadequate cardiac output, which can result in hypotension.

Transcutaneous pacing provides an immediate and effective means to increase the heart rate by stimulating the heart externally, thus improving myocardial perfusion and alleviating symptoms of bradycardia such as hypotension. It allows for temporary pacing while preparing for potential further interventions, such as transvenous pacing or identifying and treating the underlying cause of the heart block.

Digitalis administration is not appropriate in this scenario because it can further slow down the heart rate and is typically used for rate control in atrial fibrillation or heart failure, not for resolving bradycardia associated with heart block. An IV fluid bolus might help in managing blood pressure in some contexts, but it would not address the underlying issue of the heart block or the extremely low heart rate. Vasopressors can support blood pressure but would not adequately increase the heart rate in the case of complete heart block.