Final answer:
Tadeusz Kościuszko was the influential Polish engineer who helped American forces establish their winning position at the Battle of Saratoga, a pivotal moment that led to French support and was instrumental to the American victory in the Revolutionary War.
Step-by-step explanation:
The Polish engineer who played a critical role in directing where the Americans should set up camp at Saratoga was Tadeusz Kościuszko, also known fully as Andrzej Tadeusz Bonaventura Kościuszko. His understanding of fortifications and defense was one of the reasons the Americans won the Battle of Saratoga, helping to turn the tide of the war in favor of the Americans.
The American victory at Saratoga was significant as it convinced the French to recognize American independence and form a military alliance with them, providing essential military support that proved decisive in the defeat of Great Britain. Famous leaders such as the Marquis de Lafayette also joined the American cause, offering their expertise and further bolstering the American war effort against the British.