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The 20-year-old student was among four friends caught in a rip at St Kilda Beach last night and sucked about 300m out to sea.
Miss Rasmussen and two other members of the group tried to tread water once out beyond the breakers, while a fourth member of the group attempted to swim straight back in to shore - fighting the rip all the way.
All four were nearing exhaustion when the first of two surf life-savers on rescue boards - followed soon after by an IRB carrying two more volunteers - hit the water to save them.
"I can't tell you what kind of relief it is when you see someone on a surfboard coming to get you,'' Miss Rasmussen told the Otago Daily Times last night.
"We are just really thankful these people could come and help us.''
A third member of the group was receiving treatment inside a St John ambulance, also for mild hypothermia, while the fourth member of the group watched.
The four had been part of a larger group enjoying an afternoon at the beach, playing rugby and swimming in warm weather, when they found themselves in trouble about 6.45pm.
"I don't think we realised we were swimming into the rip,'' she said.
"When we realised we were in trouble, one of the boys started to swim back, to try to get help ... after that it was just a waiting game,'' Miss Rasmussen said.
The alarm was raised about 6.50pm by Phil Hudson, a water rescue squad member, who was walking his dog along the beach when he spotted a commotion.
The swimmers' friends and bystanders were gathered at the water's edge, unsure who to phone for help and instead trying to direct the group of four to safety from the shore.
Mr Hudson immediately called Stefhan Brown, another water rescue squad member, to scramble other squad members and off-duty lifeguards to the beach.
Two off-duty lifeguards paddled out on rescue boards to support those in the water and keep them afloat, until the IRB could be launched to retrieve them minutes later, he said.
All four swimmers were "extremely fatigued and cold'' by the time rescuers got to them, but the man who tried to swim straight in to shore was in the worst state, he said.
"He was just exhausted.
"We are extremely lucky we are not dealing with four fatalities,'' Mr Hudson said.
Otago Surf Life Saving search and rescue co-ordinator Max Corboy said the rescue was a good outcome but also a close-run thing.
It served as a good reminder of some basics - including the need to swim between the flags and to call police if emergencies occurred outside beach patrol hours.
Miss Rasmussen had a simple message for her rescuers.
"I just want to say thank you so much. They were absolutely fantastic.''