How did United States gain conrol over Panama?

The United States gained influence in Panama as a result of the Panamanian Revolution in 1903. The US wanted to build a canal through Columbia, which controlled the land that is now Panama. They offered Columbia a deal for a strip of land to build this canal, which Columbia refused. The US was willing to pay $10 million for this strip of land and an annual rent of $250,000. The United States then helped the people of Panama revolt against Columbia in 1903.
When Panama declared its independence from Columbia, the US helped prevent Columbia from ending the revolution. The US quickly recognized Panama as an independent country,  then offered the same deal to Panama, which was accepted, and work then began on building the Panama Canal. The US had the exclusive rights to build and operate the Panama Canal. These exclusive rights lasted until December 31, 1999, when Panama took over the operation of the Panama Canal. Thus, the US gained influence in Panama as a result of its desire to build the Panama Canal.
https://www.history.com/this-day-in-history/panama-to-control-canal