Liezl's Pythagoras Growing Post

Part 1.

What is a Pythagorean Triple ?

A pythagorean triple uses 3 perfect squared numbers to answer this question a²+b²=c²

a and b are the legs of the triangle and when their numbers are added together they equal c which is the hypotenuse of the triangle.

An example of a pythagorean triple :

Part 2.


Part 3.

LeFrog
Lefrog stands 1.5 meters from a wall where a fly is 2 meters up. if Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly ?

First you use the info they gave us:

→ lefrog is 1.5 meters from the wall
→ the fly is 2 meters up
→ his tongue can stretch 70 meters


Here is a picture of what it might look like:



















Part 4.
Bubbles, Blossom and Buttercup were playing tag outside and Bubbles was it. Blossom was 7m away from Buttercup. Buttercup was 6m away from Bubbles. How far was Bubbles away from Blossom so that she can tag Blossom?

Katarina'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 states that the two side lengths of a right angle triangle(a & b) added together equal the hypotenuse(c). A² + B² = C²

Perfect Square Chart

When you look at the chart, you have to find which two perfect squares added together will equal another perfect square.
You can find that 6² + 8² = 10².

Part Two

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=?)

Part Three

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

What do 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

Picture:

Part Four

You are stuck in a hole with an unconscious cannibal. You have to find a way to escape before the cannibal wakes up. The hole is 8m deep, so there’s no way you can climb out by yourself, so you look around and notice that there is a ladder laying on the ground beside you. You can’t lean the ladder directly against the wall because there is a pit of acid that is 4m long around the whole pit, kind of like a mote. So you have no choice but to lean the ladder 4m back. The ladder is long enough for you to get to the top of the hole. How long is the ladder?

Cedric's Pythagoras Growing Post

Part 1:
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. (Note: You need a picture, not simply text.)

A Pythagorean Triple is that 2 side lengths (also called legs- A and B) added together
equals the hypotenuse (C). Also they use perfect squares to figure the hypotenuse.
(Means no decimal answers, just a whole number) It satisfies the solution:
a squared(a2) + b squared (b2) = c squared (c2)

A Pythagorean Perfect Square Chart.



Part 2:
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=?)

First we take 2 numbers (a=6 and b=8) and solve it. Take both a and b and make it
a squared + b squared =c squared. In numbers: 6 squared + 8 squared = c squared
6 x = 36 and 8 x 8 = 64. Add them together because it has to satisfy a squared + b squared =c squared.
36 + 64 = 100. 100 goes into 10. So C = 10 and C squared equals 100.

Here is a picture on what it looks like.
I used a picture cuz my bubbleshare and any other embbed thingies wont work. Ill change it when they start working. >.>


Part 3:
Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class
(Worksheet A, B, LeFrog or Bonus Problem).

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

What you already know.

-House to the second floor window is 25 ft.

-Ladder is 10ft from house.

Pythagoras Growing Post

Part 4: Now that you have seen many Pythagorean problems, create your own word problem.

My word problemo

My mom told me to get some cups from Wal-Mart. Wal-Mart is 12 km east from my house. Suddenly i got a phone call and she told me to get milk and SafeWay which is 10 km south from Wal-Mart. Now I had to go home. When i got home, i asked myself how much i walked from SafeWay to my house i guessed 99 km. How much did i walk from SafeWay to my house? was my normal guess right or wrong?

Part 1:
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. (Note: You need a picture, not simply text.)

This is a picture of a Pythagorem Triple. A pythagorem triple says that the legs ( a and b) and the hypotenuse (c) of a right triangle follows the equation, a2 + b2 = c2. so if you add the legs together, you'll get the hypotenuse. This also shows that if you add the small square with the medium sized square, you'll get the biggest square. It uses perfect squares to find out the hypotenuse.


Proof

Perfect Square Chart

Here is the next pythagoream triple. It was quite easy to find out after you look at the perfect sqaure chart.

Part 2
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=?)

BubbleShare: Share photos - Powered by BubbleShare

Part 3
Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class (Worksheet A, B, LeFrog or Bonus Problem).

I am going to explain how we solved LeFrog. First we had the question. Lefrog stands 1.5 meters from a wall where a fly is 2 meters up. If Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly?
LeFrogs tongue had to stretch 1.98 m to eat the fly.


To figure out this problem, you first look at the question and find out the lengths of the triangle to find the hypotenuse. The lengths of our triangle was 1.5 and 1.3. It was 1.3 on one side because of the calculations i did on the top left corner. We then had to find out the length of LeFrogs tounge. We then used our formula ( a2 + b2 = c2 ). We used this formula, when we got to c, we used our calculators to find the sqaure root of the number. Finally, we found the answer to how far LeFrogs tounge had to stretch to eat the fly.

PART 4 ABOVVE !!

Pythagoras Growing Post

Part 1.
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. (Note: You need a picture, not simply text.)

What is a Pythagorean Triple ?

A pythagorean triple is a triangle that has two legs and one hypotenuse. The legs are labelled as a and b and the hypotenuse is c. The theory of the pythagorean triple is when you add the side lengths a and b it equlas c. The equation would be a² + b² = c² .

An example of a Pythagorean Triple using the perfect square chart:
























Part 2.
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=?)

BubbleShare: Share photos - Powered by BubbleShare

Part 3.

Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class (Worksheet A, B, LeFrog or Bonus Problem).

Lefrog stands 1.5 meters from a wall where a fly is 2 meters up. if Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly ?

First gather your information that you have now :

- lefrog is 1.5 meters from the wall
- a fly is 2 meters up the wall
- his tongue comes out of his mouth 70 cm from the ground

It should look something like this :

Lets start with the formula, it would be a² + b² = c². once you got the formula you start to fill in your formula with the information that you have already. a² + b² = c² now turns into 1.3m² + 1.5m² = c². With 1.3m² + 1.5m² = c² you have to square off the squared numbers to add it and so it equals c². Multiply the base numbers by itself.1.3m x 1.3m = 1.69m, 1.5m x 1.5m = 2.25m. Now you add those numbers together to equal c². 1.69m + 2.25m = 3.94m . Now you know what c² equals you just have to find the square root of it. You have to use a calculator for this so you just punch in 3.94 and press the square root button and that gives us 1.98. So now our answer is LeFrog has to stretch his tongue 1.98 m to eat the fly.


PART 4.

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

Jim was riding his bike one sunny day and he rode down the block 8 meters until he hit a bush where a dog chased him to a parking lot . If the parking lot was 5 meters away from his house how far did the dog chase Jim from the bush to the parking lot ?

Pythagoras Growing Post

Part 1

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. (Note: You need a picture, not simply text.)

This is a pythagorean triple. It uses perfect square numbers to satisfy a2 + b2 = c.

Part 2

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=?)

BubbleShare: Share photos - Powered by BubbleShare

Part 3

Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class (Worksheet A, B, LeFrog or Bonus Problem).

LeFrog

Lefrog stands 1.5 metres from a wall where a fly is 2 metres up. If Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly ?

We needed to find what c was so we first change 700 cm into 0.7m by dividing 100 into 700. We then needed to subtract 0.7 from 2m to get 1.3. With a formula a2 + b2 = c2 we plugged in the numbers so now it was 1.3 2 + 1.5 2 = c2. Then got their squared number 1.69 + 2.25 = c2. Then we added them together to get c2 which is 3.94. Since we had to find c not c2 we found the square root of 3.94 which is 1.98.

Part 4

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

A man named Johny went to buy groceries from Wal-mart which was 9 miles north from his house and after he was done he went home. Later Johny had enough money to buy a new laptop so he drove to Best Buy to buy one which was 16 miles east from his house. If Johny drove straight to Best Buy after he shopped at Wal-mart, how far would he have drove?

Kate's Pythagoras Growing Post

KATIE'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.


"PART TWO"

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?

ANSWER:

(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

THATS ALL FOR NOW :)

Pythagoras Growing Post

PART 1.

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. (Note: You need a picture, not simply text.)

What is a Pythagorean Triple ?

A pythagorean triple is an equation of a² + b² = c ² . A and b are the the legs of a right angled triangle and when the lengths of the legs are added together they equal the hypotenuse which is c. İt uses only 3 perfect square numbers for this question
a² + b² = c²

An example of a pythagorean triple using the perfect square chart:

A² + B² = C²

PART 2.

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=?)

BubbleShare: Share photos - Powered by BubbleShare


PART 3 :
Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class (Worksheet A, B, LeFrog or Bonus Problem).

Lefrog stands 1.5 meters from a wall where a fly is 2 meters up. if Lefrog's tongue comes out of his mouth 70 cm from the ground, how far does his tongue have to stretch to eat the fly ?

This would be the information they gave us in the question:
[ Lefrog stands 1.5 meters from the wall
[ a fly is 2 meters up the wall
[ his tongue comes out 70cm from the ground

It would then look like this . .

The formula for this would be:
a² + b² = c²

You would then fill in the a², b², or c² numbers that you know into the formula, and in the question they only gave us the a and b sides.
1.3m² + 1.5m² = c²

Now you have to square the numbers off by multiplying the base numbers by itself.
1.3m x 1.3m = 1.69m
1.5m x 1.5m = 2.25m

The next part is the area of the squares sides above, so when you add these two areas together it will equal the area of c².
1.69m + 2.25m = c²

So now you add these two together to get the answer for c².
1.69m + 2.25m = 3.94m

Since now we know what c² is you have to find the square root of it by using a calculator. You put in 3.94 and then press the square root button and now you have the the answer to the question.
c² = 3.94m
square root of c² = 1.98m

Lefrogs tongue has to stretch 1.98m to eat the fly.

PART 4.

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

Billy-bob is playing basketball at the court, the basket is 8 meters high. Billy-bob is at the foul line which is 10 meters away from the basket. How high does Billy-bob have to shoot the ball to get a basket?

Jessica Q's Pythagoras Growing Post

What is a Pythagorean Triple?
A Pythagorean Triple is 3 perfect unknown numbers used to satisfy:
a² + b² = c²

Example of a Pythagorean Triple:
using 1² - 10² on the perfect square chart

a² + b² = c²

6² + 8² = 10²

(6² = 6x6, 8² = 8x8, 10² = 10x10)

a² = 36 (6x6)
b² = 64 (8x8)
c² = 100 (10x10)

Part 2:
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=?)

Part 3:
Explain how to solve a Pythagoras word problem. Use one of the examples we covered in class (Worksheet A, B, LeFrog or Bonus Problem).

Worksheet A:
You’re locked out of your house and the only open window is on the 2nd floor 25 feet above the ground. You need to borrow a ladder from one of your neighbors. There’s a bush along the edge of the house, so you’ll have to place the ladder 10 feet from the house. What length of the ladder do you need to reach the window?

What I did in this word problem was, I drew a triangle which also showed the house, the ladder, and the ground. The ground and the house were the legs and the ladder was the hypotenuse. Since the question asks us to find out the length of the ladder, I used the theorem, “a²+b²=c²”. The given numbers so far were “10² feet” and “25² feet”. 10² and 25² are the legs of the triangle. After, I had to find the square root of these numbers. (10²=100 and 25²=625) I added up the numbers 100 and 625 to find out was c was. (625+100=725) Now that I had my answer, I found out what the square root of 725 was, which was 26.93². 26.93² is the length of the ladder needed to reach the window of the house.

Part 4:
Julie drives from her house to work. She starts at her house, drives 9 km south, then 12 km east to her work. How far is Julie's work from her house?