Final answer:
The nurse would assess the Pulmonary capillary wedge pressure (option 2). In heart failure, increased hydrostatic pressure within pulmonary capillaries causes fluid to be pushed into lung tissues, resulting in pink frothy sputum.
Step-by-step explanation:
To confirm the manifestation of coughing pink frothy sputum in a patient with heart failure, the nurse would assess the Pulmonary capillary wedge pressure (option 2).
In heart failure, when the left side of the heart is unable to pump out its normal volume of blood, the blood in the pulmonary circulation gets 'backed up,' causing increased hydrostatic pressure within pulmonary capillaries and pushing fluid out into lung tissues. This leads to the formation of pink frothy sputum.
The other options - central venous pressure (option 1), arterial pressure (option 3), and right arterial pressure (option 4) - are not directly associated with the manifestation of coughing pink frothy sputum in heart failure.