Be Careful How You Use the Pythagorean Theorem

There are a whole subset of triangles that have one angle that is 90° called right triangles. Often in the “real” world we see these when we are talking about things that meet the ground at this angle and then something that leans up against the thing protruding from the ground. There are many, many applications to these type of problems given the lengths of two sides one can easily find the length of the other using the Pythagorean Theorem.

I often find that my students think that the problems using this theorem are easy to understand and not too bad to compute. The problem with easy is making sure you catch the details.

I was turned onto a really great url in which a professor from the University of Utah describes an embarrassing moment that he had when he quickly tried to do a Pythagorean Theorem in his head and made a big mistake.

I have turned this mistake into a great exam problem ( I use it as an extra credit problem in my Survey of Mathematics class) when dealing with the Pythagorean Theorem.

See if you can easily figure out what the professor did wrong.

I won’t put the answer on here in case my students get lucky and find it, but I will give the hint that another way to think of:

a2 + b2 = c2


(short leg)2 + (long leg)2 = (hypotenuse)2

That should clear it all up!!

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