Final answer:
The manifestation of gastroenteritis a nurse should recognize from the given symptoms is orthostatic hypotension, which highlights the severe dehydration caused by prolonged diarrhea and vomiting.
Step-by-step explanation:
A nurse caring for a client with gastroenteritis who reports symptoms such as diarrhea and vomiting should recognize orthostatic hypotension as a manifestation of this condition. Orthostatic hypotension occurs due to the severe dehydration that can accompany the excessive vomiting and diarrhea associated with gastroenteritis. The loss of fluids and electrolytes can lead to a decrease in blood volume, causing a drop in blood pressure when the patient stands up, which is indicative of orthostatic hypotension.
Options such as hiccups, rebound tenderness of the abdomen, and shoulder pain are less indicative of gastroenteritis and more likely to be associated with other conditions. Therefore, option 3, orthostatic hypotension, is the correct manifestation related to the symptoms of gastroenteritis described by the patient.
The nurse should identify orthostatic hypotension as a manifestation of gastroenteritis from the given options since it reflects the consequences of prolonged vomiting and diarrhea resulting in severe dehydration.