!!!Pythagorean Triple!!!

OK, lets say that we know what "a" is equal to but we don't know what "b" or "c" is equal to. Lets say that "a" is equal to 3.

a = 3

b = ?

c = ?

The Pythagorean theorem states the a2 + b2 = c2. ( 2 means squared...) So what we have to do to figure out "b" and "c" using that theorem. So since we know what "a" is .......3 that means we have to square 3 which is 9. so we know that 9 + the square root of some number is equal to the square root of another number. Lets try 4. 4 (squared) is 16. 9 + 16 = ?......25. Now we need to find a number who's square root is 25. That's an easy one, 5. So this is what we know now.

a = 3

b = 4

c = 5

Now that we know all that, this is our formula: a2 + b2 = c2

32 + 42 = 52 ( 2 means squared)

9 + 16 = 25

This is what it would look like using a right angle triangle with the angles ( 3,4 and 5) normal and squared:

Part 2

To find the missing angle of a right angle triangle, first you need aright angle triangle with the other two angles....

Like so...

Also you should know that a2 + b2 = c2 can be rearranged and written like c2 - b2 = a2 or

c2 - a2 = b2.

Using Pythagoras's theory this is how you would find the missing angle.

c2 - a2 = b2

42 - 22 = b2

16 - 4 = b2

12 = b2

square root of 12 = 3.46410162

3.46410162 = b

I am going to show the house word problem.

Here is the question:

You`re locked out of your house and the only open window is on the second 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 you house, so you`ll have to place the ladder 10 feet from the house. What length of ladder do you need to reach the window?

This is how I solved it:

I used that picture to help me.

Then i wrote the formula and solved the question.

2 2 2

a + b = c

2 2 2

25 + 10 = c

2

625 + 100 = c

2

725 = c

2

(square root symbol) 725 = (square root symbol) c

26.92 = c

That's how I solved that question.

Part 4

My word problem:

"Joey is a wrecking ball operator and his next contract is to knock down a building on 21st street in New York. Since there are a lot of buildings around the building he has to take down Joey has to knock the building over with a perfect hit meaning it will come over in one hit and less debris will go flying all over the place. After a visit to the site he draws out the best place to hit the building.

He knows that the wire coming off the vehicle is 33cm long and that the wire holding the ball is 46cm long. The problem is that he doesn't know how far from the building he has to be.

How far does Joey have to be from the building?

( round your anwser to 2 decimal places and show a faction estimation)

a = 3

b = ?

c = ?

The Pythagorean theorem states the a2 + b2 = c2. ( 2 means squared...) So what we have to do to figure out "b" and "c" using that theorem. So since we know what "a" is .......3 that means we have to square 3 which is 9. so we know that 9 + the square root of some number is equal to the square root of another number. Lets try 4. 4 (squared) is 16. 9 + 16 = ?......25. Now we need to find a number who's square root is 25. That's an easy one, 5. So this is what we know now.

a = 3

b = 4

c = 5

Now that we know all that, this is our formula: a2 + b2 = c2

32 + 42 = 52 ( 2 means squared)

9 + 16 = 25

This is what it would look like using a right angle triangle with the angles ( 3,4 and 5) normal and squared:

Part 2

To find the missing angle of a right angle triangle, first you need aright angle triangle with the other two angles....

Like so...

Also you should know that a2 + b2 = c2 can be rearranged and written like c2 - b2 = a2 or

c2 - a2 = b2.

Using Pythagoras's theory this is how you would find the missing angle.

c2 - a2 = b2

42 - 22 = b2

16 - 4 = b2

12 = b2

square root of 12 = 3.46410162

3.46410162 = b

## Part 3

I am going to show the house word problem.

Here is the question:

You`re locked out of your house and the only open window is on the second 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 you house, so you`ll have to place the ladder 10 feet from the house. What length of ladder do you need to reach the window?

This is how I solved it:

I used that picture to help me.

Then i wrote the formula and solved the question.

2 2 2

a + b = c

2 2 2

25 + 10 = c

2

625 + 100 = c

2

725 = c

2

(square root symbol) 725 = (square root symbol) c

26.92 = c

That's how I solved that question.

Part 4

My word problem:

"Joey is a wrecking ball operator and his next contract is to knock down a building on 21st street in New York. Since there are a lot of buildings around the building he has to take down Joey has to knock the building over with a perfect hit meaning it will come over in one hit and less debris will go flying all over the place. After a visit to the site he draws out the best place to hit the building.

He knows that the wire coming off the vehicle is 33cm long and that the wire holding the ball is 46cm long. The problem is that he doesn't know how far from the building he has to be.

How far does Joey have to be from the building?

( round your anwser to 2 decimal places and show a faction estimation)

## 2 comments:

Haha not in your class, but nice scribe, great color and the picture really helps with your explanation, but you could make it easier for yourself by drawing a picture and taking out a camera . . . easier than paint!

why in a 345 rt triangle the squares of a +b =c2 but 3+4 =7

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