Why was the Unites states involve of the Korean and conflict?

The United States came to the aid of South Korea to repel the invasion. A rapid counteroffensive of US troops and other nations under UN mandate, returned North Korean troops north of the 38th parallel, almost to the Yalu River. Then the People's Republic of China entered the conflict on the North side, with arms support from the Soviet Union. 4

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Explanation:

The United States believed it could win and believed that China would not intervene. ... They also hoped to take advantage of the USSR's boycott of the UN to get the UN to agree to military help for South Korea. The advance of communism elsewhere made America more determined.

1) union forces launched a surprise attack.

2) more confederate troops arrived by train.

3) union forces retreated.