How are central america, philippines, and hawaii symbolic of us imperialism?

by 1890, the united states had by far the world's most productive economy. american industry produced twice as much as its closest competitor--britain. but the united states was not a great military or diplomatic power. its army numbered less than 30,000 troops, and its navy had only about 10,000 seamen. britain's army was five times the size of its american counterpart, and its navy was ten times bigger. the united states' military was small because the country was situated between two large oceans and was surrounded by weak or friendly nations. it faced no serious military threats and had little interest in asserting military power overseas.

answer placeholder because the system is messed up