Final answer:
Upon arrival along the Rio Grande, General Zachary Taylor's troops engaged with a patrolling Mexican cavalry unit, leading to American casualties that President Polk used as grounds to declare war on Mexico, setting off the Mexican-American War.
Step-by-step explanation:
When General Zachary Taylor's troops arrived along the Rio Grande, they discovered a situation that quickly escalated into hostilities. They encountered a Mexican cavalry unit that was patrolling the region. This led to a conflict where shots were fired, resulting in sixteen U.S. soldiers being killed or wounded. President Polk used this incident to declare that Mexico has invaded our territory and shed American blood upon American soil, which contributed to Congress declaring war on Mexico on May 12.
The broader context of this encounter was related to the expansionist ambitions of the United States. There was a dispute over the boundary between the U.S. and Mexico, with the U.S. claiming the Rio Grande and Mexico insisting on the Nueces River. This territorial dispute ultimately led to the Mexican-American War, which was influenced by U.S. expansionist policies and the annexation of the Texas Republic following the Texas Revolution. The Treaty of Guadalupe Hidalgo later formalized the cession of Mexican territories to the United States, resulting in substantial territorial gains for the U.S.