Final answer:
The presence of hematemesis places the ACS client at greatest risk when receiving eptifibatide due to the increased risk of bleeding and potential for shock.
Step-by-step explanation:
The client who is admitted with acute coronary syndrome (ACS) and receives eptifibatide is at greatest risk from the assessment finding of the presence of hematemesis. Eptifibatide is a glycoprotein (GP) IIb/IIIa inhibitor which works by preventing platelets from clumping together and can increase the risk of bleeding. Hematemesis, or vomiting blood, indicates upper gastrointestinal bleeding and, when combined with the anticoagulant effects of eptifibatide, can lead to a significant decrease in blood pressure, shock, and potentially fatal complications. This is a more immediate concern compared to the other options provided because it demonstrates active bleeding and requires prompt medical intervention.