At about 1.16pm on Wednesday, Whitby Coastguard Rescue Team were alerted to two people who were cut off under East Cliff, one of whom had slipped and injured their back.
Crew from Staithes Coastguard and Ravenscar Coastguard Rescue Teams were also sent to the scene.
Coastguards found the casualties and made their way under the East Cliff to their location.
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The injured casualty was taken by the inshore lifeboat back to Whitby where they were assessed by an ambulance crew.
The remaining casualty was helped back across the rocks to the East Pier by Coastguards.
Whitby Coastguard urged people to be well prepared for whatever activity you intend to undertake at the coast.
In particular remember to take appropriate equipment for the conditions and check the weather forecast and tide times before you set out.
If you see anyone in trouble at sea or on the coast, dial 999 and ask for the Coastguard.