How did the activities of the united states in latin america set the stage for war with spain?

By demanding that a dispute between Venezuela and Great Britain be sent to arbitration, the United States defended the validity of the Monroe Doctrine. (Arbitration is the settlement of a dispute by a person or panel chosen to listen to both sides and come to a decision.) The British government backed down because it needed to stay on friendly terms with the United States.The United States became involved in the Cuban rebellion against Spain, to protect American business interests.
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