She died at the scene on 29 May 2017.
Coroner Nicholas Moss told jurors at Huntingdon Town Hall the inquest would explore why two gates and a metal vertical slide, designed to ensure staff and tigers were not in the paddock at the same time, were found open.
He said the police investigation “suggested there was not any mechanical failure or fault with the gates or slides to the enclosure”.
Jurors will also examine whether the system “allowed protection against human error by the zookeeper who was in the tiger area”, the inquest heard.
King, who was working alone, entered the enclosure shortly before the zoo opened to the public at 10am.
The male tiger “would tend to urinate on the windows during the day so they need to be cleaned so the public have a good view”, Mr Moss said.
Frank York, a visitor to the zoo, saw her body from the viewing area and raised the alarm.
Keepers fetched the zoo’s tranquilliser gun, while armed firearms officers and paramedics were called to the scene.
Neither the tranquilliser nor police firearms were used as keepers were able to entice the tiger back into his run and close the slide behind him to make the area safe.
Mr Moss added: “It had been apparent from as soon as Rosa was seen that she had died.”
The inquest, which is attended by King’s parents Peter and Andrea King, heard the keeper had worked at the zoo for 13 years.
King’s mother told the inquest it was clear from the age of two that her daughter would end up working with animals.
“Rosa followed her dreams and it wasn’t very often you wouldn’t see her with a smile on her face,” she said.
Her daughter did not express concerns about working conditions, she added.
“She thought two people working together wasn’t as safe as it would be easier to become complacent,” she said.
The hearing, listed for two weeks, continues.
Additional reporting by the Press Association
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