Tier's Pythagoras Growing Post

Part1:
What's the Pythagorean triple?
For those of you who are familiar with the Pythagorean theorem, you might have came across this during your investigations.
But for those of you who aren't, a Pythagorean triple is a set of 3 numbers. In that set of numbers, when all of them are squared, adding the two lowest numbers will equal the remaining number.
*Note: after squaring, the resulting numbers must all be whole number.*

For Example, 3, 4, 5 is a Pythagorean triple.


To figure out if this set is one of the Pythagorean triple, we need to find out if the two lowest numbers squared will equal the highest number squared.

first, the formula, then we apply the measurements, then we squared the numbers that required squaring. then add a and b together.
a2 + b2 = c2
32 + 42 = 52
9 + 16 = 25
25 = 25

if the answers below equal each other, the set is one of the Pythagorean triple.

There are other sets of Pythagorean triple too.
Some of them are 6, 8, 10 and 12, 16, 20. Try them out!




Part2:
How to find the missing Hypotenuse
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Finding to missing leg:
*My Computer Won't upload the Pictures to bubbleshare, sorry.*

Its basically similar to how to find the missing hypotenuse, but instead of the formula: a2 + b2 = c2. The formula used is either c2 - a2 = b2 or c2 - b2 = a2.
pretend these are the givens:
c= 5
b= 4
a= ?

because were trying to find the missing leg a, we use the formula c2 - b2 = a2.

c2 - b2 = a2
52 - 42 = a2
25 - 16 = a2
9 = a2
3 = a

Part3:
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?

Start With the Formula:
a2 + b2 = c2

a= 25
b= 10
c= ?

a2 + b2 = c2
252 + 102 = c2
625 + 100 = c2
725 = c2
26.92 = c





Part 4:
Lucas wanted to attack Mario with his magic called "PK Thunder". Since Mario is on top of a 19 feet cliff and Lucas was 20 feet away from the cliff with 3 feet long spikes between them, he has to attack from far away. Magic's starting point is from Lucas' hands which is the same height as the spikes from the ground. How long does Lucas' attack have to travel?