Most simply, the hostages in the Iran Hostage Crisis were US citizens. As a result, the US intervened in order to protect their citizens. As for why Iranians overran the US Embassy and took its workers as hostages, this was in retaliation for the US failure to render the deposed Shah back to the Iranian Revolutionaries for "justice", which would have been a kangaroo court and execution.
because they thought they would get away with it!:D well they did
This is because the Iranian people were opposed to America's policies in Iran.
the 1979 hostage crisis
Ayatollah was the President in Iran during the hostage crisis. The hostages were taken in the US embassy in Tehran and were released 444 days later.
Iran
The US Embassy hostages in Iran.
The Iran Hostage crisis, when US diplomats in Tehran were held captive for more than a year.
The US had always been a strong ally of Shah Pahlavi, the previous ruler of Iran before the Ayatollah Khomeini's revolution, and just as the new theocracy had rebelled against the corrupt regime of the Shah, so too did they rebel against the Shah's cynical ally, the US. Of course, in so doing, they set in motion a conflict that continues to this day in various ways, and is highly destructive. It was not a smart move.
The United States debated about if they should bring the Shah into the U.S. for medical treatment. Or if they should listen to demands the Iranians wanted.
When the US did not return former Shah Mohammed Reza Pahlavi in 1979, the American embassy in Iran was attacked and several of its members were taken hostage for 444 days. This has been termed the "Iran Hostage Crisis."
Iran demanded that the US return the former Shah of Iran (Mohammed Reza Pahlavi) to Iran for a trial (which would undoubtedly result in his execution) and unfreeze Iranian government funds in Swiss Banks in exchange for the US hostages. Iran eventually got the money, but not the Shah, who died in exile in Egypt.
52 US citizens were held hostage for 444 days from November 4, 1979 to January 20, 1981, after a group of Islamist students and militants took over the Embassy of the United States in support of the Iranian Revolution. This was the Iran hostage crisis. Carter sent a delat team but the mission was aborted because an airplane struck another aircraft. Bad press allways did the thing but there were other things that did worse in Carter's image.
Radical followers of the Ayatollah Khomeini overran the U.S. Embassy and took Americans hostage to protest the admission of the Shah of Iran into the United States for medical treatment, or because the US was spying on Iran from inside the embassy.