Nathaniel's Pythagoras Growing Post

Third Growing Post!

What Is A Pythagorean Triple?

A Pythagorean Triple is three square numbers in which when two square numbers are added they equal another square number. The formula being Asquared + Bsquared = Csquared. Asquared and Bsquared are the legs of the trianged. Csquared is the hypotenuse.

For example 3squared + 4squared = 5squared. Which equals 9 + 16 = 25

Another Pythagorean Triple is 5squared + 12squared = 13squared. Which equals 25 + 144 = 169

How to find a missing leg/hypotenuse

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How to solve a word problem!

Here is a word problem that I will use to help me explain how to solve a word problem.

You picked up a ground ball at first base, and you see the other team's player running towards third base. How far do you have to throw the ball to get it from first base to third base, and throw the runner out.

There was also a picture



The key thing you look for is numbers! They usually are very important. The first thing you should underline is First Base because thats where you are. And then third base you underline because thats where the other person is going to. And the question, you have to find out how far you have to throw the ball. The picture shows that from 1st base to 2nd base is 90 feet, and 2nd base to third base is 90 feet. If you look at it, it is a right triangle! The legs being 90 feet and the hypotenuse being first base to third base! All you have to do is solve for the hypotenuse.

a = 90 feet
b = 90 feet
c = ?

a2 + b2 = c2
90squared + 90squared = c2
8100 + 8100 = c2
16200 = c2
square root of 16200 = c
127.28 = c

My Own Word Problem!

Stretch Armstrong sees a little boy crying because his ball got stuck on the roof, so he decides to help get the ball down. He is 10 feet from the wall, and the roof is 40 feet high, how far does Stretch Armstrong have to stretch his arm to reach the ball if his arm is 20 feet high.

Derrick's Pythagoras Growing Post

- Pythagorean Triple ?
- Three numbers a, b, and c that satisfy a² + b² = c² are called Pythagorean Triples.
- some Pythagorean triple other than 3,4,5 is 5,12,13

This picture shows how a pythagorean triple works. Its three squares making a right angle triangle in the middle.



Example:



Following the formula a² + b² = c2 we got 5² +12² = 13².

a²= 5 - 5²
b²= 12 - 12²
c²= 13 - 13²















a² + b² = c2
5² +12² = 13²
25 + 144 = 169




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?

PART III

In this problem, it says to find the length of the ladder to reach the window. (Ladder: a, house: b, ground: c) In the picture, you can see a triangle. (a²+b²=c²) The length between the window to the ground is 25 feet, the length between the house to the ladder is 10 feet because of the bush, you have to find how long the ladder has to be. (25²+10²=c²) Next you have to find the square root of these numbers. (25² = 625, 10² = 100) An easy way to find the length of the ladder is just by adding the square roots together. (625+100=725) Then, you have to find the squared number of 725. (√725 = 26.93²) Now that you have the square root of 725, 26.93 feet is how long the ladder has to be to reach the window.

PART IIII
Jordan and Jon are playing a 2 on 1 volleyball game with Jessica. Jessica served the ball to Jordan with a distance of 12 m. Then Jordan passed the ball to Jon with a distance of 5 m. How far does Jon have to hit the ball to Jessica?

Danica's pythagoras growing post

This is my word problem

Danica's Third Growing Post

The pythagorean theorem states that the legs (a & b) and the hypotenuse (c) of a right triangle obey the following relationship a squared + b squared= c squared.

Perfect Square Chart
1 square= 1
2 squared=4
3 squared=9
4 squared=16
5 squared=25
6 squared=36
7 squared=49
8 squared=64
9 squared=81
10 squared=100

2)
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This is a word problem we had to solve in class

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Kiahna's Pythogoras Growing Post

Kiahna's Third Growing Post!




This is an example o some of the work we did in class!


The first one on the top left corner says:
The pythagorean theroen states that the legs are a2 and b2. The hypotenuse c2. obey the following relaionship. A2+B2=C2.

The second one on the top right is:
A2+B2= C2

The third one on the bottom left says:
The pink one is 3x3=9.
The outside blue is also nine
so the pink is the outside of the bigger triangle
Kind of like hair.

This is Question # 1
Pythagorean Triple

a2= 36

b2= 64

c2= 100

You have to use a perfect square chart from one to ten
12 1x1 1
22 2x2 4
32 3x3 9
42 4x4 16
52 5x5 25
62 6x6 36
72 7x7 49
82 8x8 64
92 9x9 81
102 10x10 100
2 stands for squared




Question #2

Find The Missing Number

You use the perfect square chart to figure this out but this time you can use it from 1-to whatever you want. I used 1-30.

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12 1x1 1
22 2x2 4
32 3x3 9
42 4x4 16
52 5x5 25
62 6x6 36
72 7x7 49
82 8x8 64
92 9x9 81
102 10x10 100
then just go up to 30.


Question #3

Word Problem Letter B


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My Word Problem

Harry has 9 cm and 10 cm. He i useing the 9 cm for a2 and the 10cm for b2. He needs help finding the c2 . You ahve to find the missing side so do whatever you do for it and find the answer.

Andrea's Pythagoras Growing Post

TRIPLE PYTHAGOREAN THEOREM:


Part One:
A Pythagorean triple consists of three positive integers a, b, and c. A right triangle exists with legs a, b and the hypotenuse c. A Pythagorean Triple is three square numbers in which when two square numbers are added they equal another square number.

Other Pythagorean Triples:

(5 12 13)

(7 24 25)

(8 15 17)

(9 40 41)

(11 60 61)

(12 35 37)

Part Two:

FIND THE MISSING LEG:

FIND THE MISSING HYPOTENUSE:

Part Three:





Part Four:

Lindsay is in math class and is learning about the pythagorean theorem (a² + b²= c²). The question on the board is asking how can you prove that 3² + 6²= 9². Expalin if the answer is right or wrong. Use a picture to show your work.

OTHER EXAMPLES:

Kierra's Pythagoras Growing Post.//

Pythagorean Triple

is three any 3 numbers that can fit A(squared)+ B(squared)=C(squared) is called the pythagroean triple.

If you have:

a(squared)=8

b(squared)=6

c(squared)=10

So in a pythagorean triple a + b would be the legs in the triangle and c is always the hypotenuse:

The picture shows you how a(squared) + b(squared)=c(squared)

In this example: 8(squared)=64 + 6(squared)=36 = 10(squared)=100 or (64 + 36 = 100)

Part 2 :

Part 3:

For part 3 I chose to explain the baseball diamond problem:

You’ve just picked up a ground ball at first base, and you see the other team’s player running towards third base. How far do you have to throw the ball to get it from first base to third base,and throw the runner out?

Each side of the baseball diamond is 90ft

As you can see in the picture all you had to do was cut the diamond in half from 3rd base to 1st and get the right triangle. From there all you had to do was figure out side C which was the distance from 3rd to 1st base. and to figure of  C all you did was use A(squared) + B(squared) = C(squared)

Part 4:

My Dog Bob

My dog bob is a really long tongue and he is standing on the floor, 3 meters from the cookie cupboard. The cupboard is 5 meters tall and the cookies are at the top.Bob's tongue is 1 m. off the ground from where he is  standing. How far does Bob have to stretch his tongue to get the cookies ?

Megan's Scribe Post

Today in class we continued with our new unit The pythagorean Theorem. We had to find out the Pythagorean Triple using only up to 5 on our perfect square chart. The pythagorean triple is 3,4 and 5.

(Ex. 32(squared) + 42 = 52. = 9 + 16 = 25. A2 + B2 = C2. The first, second, and third numbers show A2, B2 and C2. (squared).

32 or 9 = A,

42 or 16 = B2,

and 52 or 25 = C2

Then later during class we showed the pythagorean triple in 3 pictures for better understanding.

This is called Proof #1

1) This picture shows that the pythagorean triple helps show A2 + B2 = C2.

2) Shows that 32 + 42 = 52 using...well, squares to show that both A and B makes C.

3) The shaded parts around the 42 shows that 52 was made by adding 32 to 42.

Well, thats it!!! XD (Feel like using red now!)