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Using the Pythagorean Theorem to find a Missing Hypotenuse - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

The hypotenuse of a right triangle is the side that is opposite of its right angle. Sometimes we have problems that ask us to find the missing hypotenuse of a right triangle. We can use the Pythagorean theorem to find the hypotenuse, but only if we know the length measure of the two legs.

The Pythagorean theorem says that if
you have a right triangle where you
know your two legs and a hypotenuse where
the legs are the sides adjacent
to your right angle and the hypotenuse
is the side that is opposite the
right angle, there exists this relationship
that if you take one of the
legs N squared and if you add it to the
other leg, N squared, that's going
to equal the square of the hypotenuse.

So if you're trying to solve for one of
these variables, you're going to need
two of them.
And the easiest problem that you're going
to see using the Pythagorean theorem
is one where you know your two legs and
you're trying to find your hypotenuse.
The reason why this is the easiest is because
all you have to do is substitute
in and then you can square it equal
C squared and then you're going to
have 13 equals C squared and you can
take the square root and C equals
the square root of 13.

So I didn't have to do any
manipulation there.
All I had to do was plug in my two legs
and then solve for my hypotenuse.

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