ShmoopTube

00:03

Pythagorean Theorem, a la Shmoop.

00:07

Peter Pan has a problem. [Peter awakens in bed]

00:09

No, no…another problem.

00:11

He’s had his shadow a long time, and it’s been run ragged.

00:14

Time to bite the bullet… he’s due for a new one.

00:17

But he doesn’t just want a replacement. He’s in the market for something bigger and better. [Peter browsing a supermarket]

00:22

Michael and John have been introducing Peter to a little pre-algebra…

00:25

…and Peter decides he can pick out his new shadow by using the Pythagorean Theorem…

00:30

…which says that, when dealing with a right triangle, the square of one leg of the triangle,

00:36

added to the square of the other leg, will equal the square of the hypotenuse.

00:40

Or expressed algebraically a-squared + b-squared = c-squared.

00:45

Fortunately for Peter, he and his shadow form a perfect right triangle. [Peter stood with a perfect triangle and Wendy appears]

00:49

He knows that Wendy wants the tippy-top of his head to be exactly 10 feet away from the

00:54

the top of his shadow's head at all times.

00:57

Peter is six feet tall. His height squared is 36…

01:01

…while the desired distance from the head of his shadow squared is 10 squared…

01:05

…or 100.

01:06

So Peter needs his shadow to be a number that, when squared… [Floating numbers]

01:09

…makes up the difference between 100 and 36.

01:13

So let's do the math.

01:15

100 minus 36 is 64…

01:18

… and the square root of 64…is 8.

01:21

Checking to make sure that works out, we’ve got a triangle with sides that are 6, 8 and 10 feet long… [triangle with all measurements of each side]

01:27

…and 6 squared plus 8 squared comes out to 100…

01:30

…which is the same as 10 squared.

01:32

Peter is a lost boy no longer!

01:34

The neighbors are very jealous… [Peter in his bedroom and Captain Hook appears]

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