I found an explanation of the Pythagoras sentence and they explained it with this picture:
The statement is that this results in c² + b² = a², so mathematically the statement is correct for the given drawing, and I can't really complain.
My concern is that someone with a visual memory might remember the drawing well and at the same time remember the Pythagoras sentence a² + b² = c² from school (at least for me in 1995, where it has been hammered into the brain), so in the end, he gets it wrong.
Is there a convention that the corner at the right angle should be named C, so that c becomes the longest side and the Pythagoras sentence becomes a² + b² = c² as we're used to?
I'm looking for "normative" references like guidelines from a mathematician association or similar which I could use when I get in contact with the training provider who ddesigned that thing.
People try to simplify math concepts, and unfortunately they often simplify so much that the meaning and purpose of the activity get lost.
Back in the Dark Ages when I went to school, we were taught: "The square on the hypotenuse equals the sum of the squares on the other two sides." While we are at it, the hypotenuse is the side opposite the right angle. The right angle is vital to the theorem. This is simple, describes the visual image exactly, and says what it means to say. The newer idea of giving the theorem as a formula allows students to write less and was supposed to be more "efficient". Considering how math test scores have been dropping for decades, we need to re-evaluate that "efficiency".
Unfortunately, as you rightly note, many people memorize the letters without attaching them to the meaning. Then when the letters change the students are lost. This kind of teaching is anti-mathematical. The whole point of all that algebra is that you can abstract from physical meaning to symbolic letters, and go back from abstract letters to physical meaning. Memorizing formulas with no relation to their application is counterproductive.
When I am teaching students about Pythagoras, I always give problems with different letters and never a,b, c. If I ask them to explain the theorem, I warn them ahead of time that simply writing a formula without referring to a concrete object will get negative marks. They certainly grumble a bit but after a little while they are doing math a lot better.