Final answer:
The county sheriff serves as the sole legal authority over vast geographical areas within county boundaries and is responsible for a wide array of law enforcement tasks.
Step-by-step explanation:
The local law enforcement official often serving as the sole legal authority over vast geographical areas is typically the county sheriff. Sheriffs are elected officials who are responsible for maintaining peace and enforcing the law within county boundaries. Their duties can cover a broad range of tasks, such as responding to emergency calls, working in the local jail, and patrolling various parts of the county. Unlike state police, who have authority to enforce statewide laws, or federal officers, who deal with specific matters pertaining to federal law, the sheriff's jurisdiction is confined to their respective county.