Sunday, March 16, 2008

Kate's Pythagoras Growing Post


"Part One"

Task: Describe what a Pythagorean Triple is and use your perfect square chart from 1 squared to 10 squared to find another one other than 3,4,5.

What is a Pythagorean Triple?

A Pythagorean Triple is a theory that says the two side lengths of a right angle triangle added together = the hypotenuse. The equation for that would be:

A² + B² = C²

To find the next Pythagorean Triple you look at your perfect Square chart to figure out which will work.

When you look at that you have to decide which two perfect squares added together will equal to another perfect square.

Right away you can tell that 6² + 8² = 10²

Then you can draw it out.

You can also show it this way:

A² + B² = C²
6² + 8² = 10²
36 + 64 = 100

It all means the same thing.


Task: Using embeddable web 2.0, describe how to find the missing side of a Right Triangle using the Pythagorean Theorem, show how to solve both for a missing leg and the hypotenuse (note: you may use numerical examples ie. a=4 b=6 c=?)

My Bubble Share

BubbleShare: Share photos - Play some Online Games.

" Part Three "

Question: You're locked out of your house and the only open window is on the second floor, 25
ft above the ground. You need to borrow a ladder from one of you rneighbours. There's a bush along side the edge fo th ehouse, so you'll have to place the ladder 10ft from teh house. What length fo the ladder do you need to reach the window?

So first you should lay out the information you know.
>The Window is 25 ft above the ground
> There is a bus that goes out 10 ft on the ground
>You have to lean the ladder on an angle to get it to the house
>You're trying to figure out how long the ladder is

Then Try to Draw it out... Like this...

You probably noticed its is a right triangle. After noticing that you can use the Pythagorean theorem to solve what C is. ( C is always the side the right angle is pointing to with its corner.) Since you know that A² + B ² = C ² you plug in the info you know already

The Theorem
A² + B² = C²

Then you put the numbers in you know. A² & B² can be swapped it doesn't matter what number is where. I always put the smaller number in A.
10² + 25² = C²

Then you have to square the numbers as the theorem states. All you have to do is take the base number and multiply itself by itself.
10 x 10 = 100
25 x 25 = 625

Then you put those numbers into your equation.
100 + 625 = C²

Now all you got to do to find out what C² is is add the two numbers together.
100 + 625 = 725

That means that C² is 725
C² = 725

Now you have to find the square root of that number to find out how long the ladder is.
The square root of 725 is :

Fraction :

" Part Four "

Task: Now that you have seen many Pythagorean problems, create your own word problem.

My Word Problem

>>Giggle the snake was slithering through the park one day to meet up with his friend Shout. They started to argue about who was longer. Giggle said he was so long that he could reach all the way from the edge of the tree stump to the sticker half way up the side of the outhouse. If the outhouse was 8 feet tall and the stump was 6 feet away from the outhouse how long would Giggle have to be to be able to reach from the bottom edge of the tree stump to the sticker on the side of the outhouse?


(Highlight to see text. It's in white so you don't see it until you want to)

This is all in words becuase I didn't know how to hide pictures.

If the outhouse is 8 feet tall & the sticker was half way up that means the sticker is 4 Feet high. Now you know that one of the legs is 4. The right angle is where the ground meets the outhouse.

To the edge of the tree stump is 6 Feet. To find the hypotenuse or how long Giggle's is all you got to do is follow this:

A² + B² = C²

4² + 6² = C²

16 + 36 = C²

C² = 52

The square root of 52 is 7 3/15 or 7 1/3 OR 7.21


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