Final answer:
The colonists gained strategic control over the heights around Boston, notably Breed's Hill and Bunker Hill, which allowed them to use artillery against British positions and eventually force the British evacuation in 1776.
Step-by-step explanation:
During the siege of Boston, the colonists gained control of strategic heights, specifically Breed's Hill and Bunker Hill, surrounding the city. These hills allowed the Continental Army to place artillery in a commanding position overlooking both Boston and the harbor. By doing so, they could effectively threaten British ships and fortifications, which proved crucial, as the British were unable to counter the elevated position of the colonial cannons. This control forced the British to evacuate Boston on March 17, 1776, marking an early and significant victory in the American Revolutionary War. The capture and use of these heights demonstrated the importance of terrain and logistics in military conflict, lessons that would be valuable throughout the remainder of the war.