How did the gulf of tonkin resolution affect the course of the vietnam war

It increased involvement because it allowed the US President to make military actions, like increase troops, without formal declaration of war.

Explanation:

The Gulf of Tonkin Resolution, passed by Congress in August, 1964, after alleged attacks on two US naval ships in the Gulf of Tonkin.  The key wording in the resolution said:

Resolved by the Senate and House of Representatives of the United States of America in Congress assembled, that the Congress approves and supports the determination of the President, as Commander in Chief, to take all necessary measures to repel any armed attack against the forces of the United States and to prevent further aggression.

That resolution served as a blank check for President Johnson to send troops to whatever extent he deemed necessary in pursuance of the war.  Between 1964 and the end of Johnson's presidency in 1969, US troop levels in Vietnam increased from around 20,000 to over 500,000.

always include the steps and/or background required to get to the final answer. let’s other people understand and solve future problems on their own.

well i'm late but i think its: b, c, and e