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 Question from Britta, a student: Please, give me some complex real life situation examples where the pythagorean theory is used. It must be a grade 8 or grade 9 level of thinking as that is what is my teacher's demands.

Well, I'm sure your teacher wants you to find them yourself too. But maybe a few hints would be OK?

Think about situations where you know two sides of a right triangle

and you want to know the third. The right angle could come about because one side next to it was the ground and the other was vertical; because one side was a distance North and the other a distance East; because they were walls of a room meeting at a corner; because you had cut or folded a corner of a sheet of paper or cloth; or for other reasons.
The theorem tells you that A2 + B2 = C2

The hypotenuse (long side) might be the length of a ladder, or pole, or whatever, that you knew, and you might be able to measure B on the ground but not A.

The theorem only holds if the angle is right; if you knew A,B,C you could check whether you had a right angle. (Look up Egyptian surveying on Google.)

Now, you make up some stories using ideas like that.

Good Hunting!
-RD

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.