Why did the us enter the war on the side of the triple entente?

Essentially, you are asking why the USA entered WWI on the side of England, France, and Russia.

There are two main reasons why the USA entered WWI. The first was Germany's decision to renew unrestricted submarine warfare in the Atlantic Ocean. The United States was quite upset with Germany's use of submarines to sink merchant traffic headed to England and France. The U-boats sank or damaged a number of high-profile civilian targets (the Lusitania, for one) on which dozens or even hundreds of US citizens were killed. The Germans had stopped unrestricted submarine warfare for most of 1916, I believe, just so that the US would not enter the war. By early 1917, though, Russia was beginning its collapse and Germany was getting strangled by Britain's effective blockade of German ports. So, Germany elected to restart its submarine campaign.

(As an aside, Britain also had a policy of stopping and seizing merchant ships headed for Germany. The difference was that Britain didn't sink the ships it caught. It brought the ships and cargoes home and then reimbursed the owners for the loss. Germany's lack of a viable long-distance surface force and port access precluded it from taking these steps. For Germany, it was U-boats or nothing.)

The second, and arguably more important element was known as the "Zimmermann Affair." In late 1916 or early 1917, the US State Department intercepted a cable from Germany to Mexico wherein Germany promised to return all the land Mexico lost to the US in the Mexican War (and other transactions, such as Texas Independence and the Gadsden Purchase) to Mexico in exchange for an alliance with Germany against the US. Once this information was publicized, US public turned sharply away from isolationism and towards war against the Triple Alliance (Germany, Austria-Hungary, and the Ottoman Empire).