Question

How did President Roosevelt’s “big stick” policy affect the construction of the Panama Canal?

The United States helped Panama declare independence from Colombia, then negotiated for the canal.
The United States helped Colombia declare independence from Panama, then negotiated for the canal.
The United States used military force to annex Panama, then demanded that the canal be built.
The United States used economic sanctions to hurt Panama, then demanded that the canal be built.

Answer 1

The United States helped Panama declare independence from Colombia, then negotiated for the canal.

Roosevelt used "big stick" diplomacy (naval power) to block Colombian forces from suppressing Panama's 1903 revolt, quickly recognized the new republic, and then secured the Hay–Bunau-Varilla Treaty granting the U.S. the canal zone and rights to build the Panama Canal.