Final answer:
George Washington's accomplishment following the Battle of Bunker Hill was the eventual capture of Boston, using cannons from Fort Ticonderoga to drive out the British forces.
Step-by-step explanation:
One of George Washington's accomplishments after the Battle of Bunker Hill in 1775 was to capture the city of Boston from British control. This was achieved by using the cannons from Fort Ticonderoga to compel the British to evacuate. Despite General Gage's and his generals' efforts to hold Boston and its strategic high grounds at Breed's Hill and Bunker Hill, their plans were thwarted. Washington, whom the Second Continental Congress had appointed as the commander-in-chief of the Continental Army in June 1775, proved adept at laying siege and pressuring the British, which eventually led to their withdrawal from the city.
The Battle of Bunker Hill, while a technical victory for the British, resulted in very high British losses and did not break the colonial siege of the city. This contributed to Washington's successful strategy to eventually force the British evacuation. Washington's leadership and the army's growing capabilities showcased early American resilience and provided a significant morale boost to the Patriot cause.