Welcome to The Pythagorean Theorem: Finding the Length of the Hypotenuse (with Decimals) with Mr. J! Need help with the Pythagorean Theorem? You're in the right place!
Whether you're just starting out, or need a quick refresher, this is the video for you if you're looking for help with the Pythagorean Theorem. Mr. J will go through two examples of right triangles and explain how to use the Pythagorean Theorem to find a missing side length.
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In this video I'm going to cover how to find the length of the hypotenuse using the Pythagorean
theorem and we're going to be working with decimal side lengths. Now remember we use the equation a
squared plus b squared equals c squared with a and b being the legs. It doesn't matter which leg is a
and which leg is b and then c is always the hypotenuse. If we know the lengths of two sides
of a right triangle we can use the Pythagorean theorem to find the length of the third side.
Let's jump into our example where we have a right triangle and the lengths of the legs are given so
we need to find the length of the hypotenuse. Let's call this leg a and this leg b and then
the hypotenuse is always c. So we are going to use a squared plus b squared equals c squared.
Now we can plug in what we are given and work through this equation in order to figure out
the length of the hypotenuse. a is six and seven tenths feet so let's plug that in so six
and seven tenths squared plus b is 15 and two tenths feet so let's plug that in so 15 and
two tenths squared equals c squared. Now we just continue to work through that equation until we
out what c equals. Six and seven tenths squared gives us 44 and 89 hundredths plus 15 and two
tenths squared gives us 231 and four hundredths equals c squared. Now we can add what's on the
side of the equation so 44 and 89 hundredths plus 231 and four hundredths that gives us 275
and 93 hundredths equals c squared. Now we need to isolate c and figure out what c equals.
Since c is being squared we can isolate c by taking the square root of c squared.
So the square root of c squared. Whatever we do to one side of the equation we must do to the other.
So we need the square root of 275 and 93 hundredths as well. c is now isolated so we have c
equals and then as far as the square root of 275 and 93 hundredths that is not a perfect
square so we don't end up with a whole number answer. So c equals the square root of 275
and 93 hundredths. Now we can write that square root as an approximate rounded decimal. The
square root of 275 and 93 hundredths is irrational. The decimal never stops and it doesn't
repeat. So again let's round it. Since the side lengths of the right triangle go to the tenths
place let's round this decimal to the tenths place. So the square root of 275 and 93 hundredths
is 16.61 and this continues on. So I wrote it to the hundredths place that way we can round it to
the tenths place. There's a six in the tenths place with a one to the right in the hundredths.
So this rounds to or is approximately 16 and six tenths. So that means that c and I will put c
first here so c is approximately 16 and six tenths and this is feet. The hypotenuse the unknown or
missing side length of this right triangle is approximately 16 and six tenths feet. So there
you have it there's how to use the Pythagorean theorem in order to find an unknown or missing
side length and specifically in this example we needed to find the length of the hypotenuse.
I hope that helped thanks so much for watching until next time peace
