Why did the us intervene in the korean war

The USA went to war in Korea for three reasons.  

The first reason was the ‘Domino theory’.   Salami tactics in eastern Europe was not the only place where Communists were coming to power.  In the Far East, too, they were getting powerful China turned Communist in 1949.   Truman believed that, if one country fell to Communism, then others would follow, like a line of dominoes.   He was worried that, if Korea fell, the next ‘domino’ would be Japan, which was very important for American trade.   This was probably the most important reason for America’s involvement in the war.

The second reason was just to try to undermine Communism.   President Truman believed that capitalism, freedom and the American way of life were in danger of being overrun by Communism.   The Truman Doctrine had been one of ‘containment’ – stopping the Communists gaining any more territory.   In April 1950 the American National Security Council issued a report recommending that America abandon 'containment' and start 'rolling back' Communism.   This led Truman to consider driving the Communists out of North Korea.

Finally, Truman realised the USA was in a competition for world domination with the USSR.   By supporting South Korea, America was able to fight Communism without directly attacking Russia.

Hope this helps.