Final answer:
The Panama Canal's construction resulted in significant maritime travel benefits, with a decrease of over 8,000 miles across voyages, and an enduring impact on trade and military logistics, despite the high human and political costs. The strategic advantages were seen during World War I, indicating that the benefits were considered worth the obstacles.
Step-by-step explanation:
Whether the benefits of building the Panama Canal were worth the obstacles is a complex question that involves considerations of engineering triumph, human cost, strategic military and economic benefits, and political ramifications. Colombia initially rejected the United States' proposal, anticipating they could secure a better deal once the French company's rights expired. Ultimately, through the support of Panamanian independence and consequent treaty arrangements, the U.S. acquired the necessary land.
The canal's construction, completed in less than ten years by the U.S., came at the expense of many lives but yielded a significant reduction in maritime travel time, cutting more than 8,000 miles off voyages between the Pacific and the Atlantic Oceans. Strategic advantages became immediately evident with the outbreak of World War I, as the canal permitted U.S. warships and cargo to avoid the treacherous journey around Cape Horn.
Roosevelt's determination and strategy in acquiring the canal zone through the assistance of a Panamanian revolution and subsequent treaties resulted in a bitter relationship with Latin America due to the perceived duplicity of the U.S.
Nevertheless, the canal stands as a remarkable feat of engineering, with contributions from key figures like George Washington Goethals and Dr. William Gorgas, who overcame geographical and health challenges that had thwarted previous attempts by the French. Despite political and human costs, the eventual consensus leans towards the canal's benefits outweighing the obstacles, evidenced by its enduring role in global trade and military logistics.