A passenger aboard a Whitby Whale Watching vessel photographed one of the whales' carcasses during a boat trip this week, and a birdwatcher took pictures of the other two, one of which appeared to have been struck by a boat.
In the images, taken by Ryan Chadwick and Ian Boustead, fishing wire can clearly be seen encircling the bodies of two of the cetaceans, one of which is believed to be a juvenile whose distressed mother was nearby. The other had head injuries consistent with a collision.
The carcasses are floating near Staithes and Sandsend and are beginning to decompose and bloat. One has come to rest near Whitby Pier.
Minke whales are now a regular sight off the Yorkshire coast, and they follow shoals of herring. They are also attracted to the feeding grounds off Flamborough Head.
They are commonly seen between Staithes and Whitby between June and October each year, but it is not the first time one has been found dead in such circumstances.
At least three other whales have been killed in separate incidents involving fishing gear off the Yorkshire coast in the past decade.
Many of the entanglements are caused by lobster pot chains, which are laid by fishermen who set lobster pots on the seabed, connected together and attached to buoys on the surface.
Others are due to discarded fishing tackle from trawlers.
In these instances, whales drown because they are unable to free themselves and become exhausted.
Whale-watchers in the area also believe that whale numbers are decreasing as herring stocks become depleted by commercial fishing.
Mr Chadwick, a wildlife artist from a family of fishermen, was on the Whitby Whale Watching boat on Tuesday when he spotted the first of the corpses.
"We were about 15 miles out when we saw it. The skipper had already told me that it hasn't been as busy for whales this year, as supertrawlers have been in the area and there isn't as much food for them.
"We think it had only been dead for about two hours, as it hadn't swollen up. The mother was nearby and she was swimming around and blowing in distress.
"Two more were later found, one rotting near Whitby Pier with fishing line around its neck. The other looked like lobster pot wire. The skipper thought one of them might end up beaching in the Runswick Bay area, judging by the direction it was drifting.
"We had seen 50 bottlenose dolphins on the trip, but everyone was just so depressed by the sight of the whale."
Mr Chadwick recalls a previous minke whale death in 2013, when a female beached in the area having become entangled in fishing equipment.
"The fisherman who was responsible was traced and he was really upset - many of them do care about the whales, but these supertrawlers just don't.
"People often say Brexit will make a difference, but it won't. Many of the trawlers fishing in the North Sea aren't from EU member states anyway. There's nothing stopping someone who is Dutch, for example, registering a boat here and fishing out of Scarborough. The wildlife is paying the price."
He believes the Yorkshire coast is unlikely to again attract rarer species such as fin whales, one of the world's largest.
"One of the skippers saw a fin whale in 2014, around 86ft in size. But the stocks have been plundered now, the humpbacks are staying in Norway. They follow the food."