Hey and welcome to teacher Schmidt. We're doing math together today. We're working on the Pythagorean theorem. And today we want to calculate a map. In the last video, we calculated a hypothesis. And today, one of the two cadets is doing something like this. They need their triangle, and it's very important that it has a right angle. Otherwise, the Pythagorean theorem doesn't work. Very briefly, label the corner points of ABC counterclockwise in capital letters, opposite a, b, and c. And in exactly this constellation, the Pythagorean theorem applies, as you learned it. So, square + b squared equals c squared. The problem with this naming is that it's not always valid. That's why I recommend, and we've already discussed this in the other videos, packets to the square. Catheter to the square equals the time to the square. So, what was the hypothesis again? It's very simple. The hypothesis is always opposite the right angle. That's why you can find the hypothesis so easily. And the other two, the ones that enclose the right angle, are called We each have a card, so it's much easier to form this sentence, so packets to the square plus card to the square is hypothesis to the square, that's the beginning, and now a couple of examples, this time change it like the 3 a little bit, it remains a sketch, so as I said, nothing to measure and so on, and this time there are new letters, always more like s&t, and you see for the first time the problem is, what is that, okay, and we know this time that in our example it is now ten centimeters long and small, now x 6cm, okay, good, and now we should calculate, so it is wanted, okay, how do we proceed? First, we write down our approach again, if you want, always write down the first sentence, so packets to the square plus card to the square equals t muse to the square, then we can put the whole thing at the top, so hypothesis to the square - one of the two packets to the square is catheter to the square, okay, now we've done the worst, now we just need to insert the bracket again, ten centimeters, bracket closed - like this In this case it says six centimeters, so brackets open, 6 cm, brackets closed to the square and that is the result, okay, so ten times ten is 100 centimeters times centimeters is centimeters to the square of 2 - square number of 6, 36 cm to the square of two are square centimeters, so 100 - 36 is 64, expect 10 centimeters and now we know the area, but of course we want to have the side, so the root of 64 square centimeters and we can do that again in our heads, the same numbers again, just eight centimeters and then we have done it, at this point you will recognize a pattern and that is very, very important, whenever we calculate a chain, we don't have to do anything other than a hypothesis to the square - the catheter that goes over to the square, of course, and then the map we are looking for comes out to the square, so we enter the whole thing into the calculator because we really have to, 10 squared - 6 squared is equal to 64, second calculation step 4 and Root of 64 and that is 8 again for comparison the quick way the root of ten squared - 6 squared if we enter it like that we immediately have the result result eight okay we've done that too let 's do one last example again a sketch and I would recommend you actually the few seconds it takes for a sketch I would always take that then you have it visualized a bit better if you have problems with it this time it's completely crazy xyz so a completely crazy sequence and we know this time what we are taking we know that y is equal to five centimeters and we know that it is equal to four centimeters and what we are looking for is z okay so I know you can do it anyway let's do it step by step first we write down the basic formula and that is map to the square plus parcel to the square equals hypo t muse to the square now we rearrange the whole thing because you can see z we are looking for a map so our formula is mortgage muse to the square - a map to the square and you get a map to the square next step insert our hypothesis is 5 cm so open bracket five centimeters close bracket to the square - in this case four centimeters in brackets to the square and you get our result okay so it sounds like in your head of course 15 square is around 20 centimeters to the square is square centimeters -14 square we know the square numbers by heart 4 x 4 16 square centimeters so 25 16 is nine square centimeters and the square root of nine square centimeters we can do that in our heads too that's three centimeters and there we have the task again well you see all in all it's a very simple thing if you look for a map then you calculate the muse to the square - map to the square no matter which letters are used it always works and you always find the hypothesis opposite the right angle okay that's it