Sunday, March 16, 2008

Angelo's Pythagoras Growing Post

A Pythagorean Theorem is when the legs of a right triangle ( a & b ) and the hypotenuse obey the following relationship " a2 + b2 = C2."

A Pythagorean Triple is a right triangle that uses a set of numbers (1,2,3,etc...) that satisfy a2 + b2 = C2. The set of numbers can't have any decimals For example, 3squared + 4squared = 5squared.Another way to say that is, 9 + 16 = 25.

I had to figure out another Pythagorean Triple using only the Perfect Squares up to ten. The perfect squares are:
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
The next Pythagorean Theorem after 3 squared + 4 squared = 5 squared is, 6 squared + 8 squared = 10 squared. I proved it in three different visual ways.
The first one I used the right triangle. It is clear that the legs will add up to the hypotenuse.

The second way, i proved it in squares. It is clear that 36 squares (6 squared) + 64 squares (8 squared) will equal 100 squares (10 squared).

The third way, I showed it in squares again. You could see that the a2 and b2 fits in c2 perfectly.

Part 2:
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For the missing hypotenuse, I first wrote down what i knew then began the Pythagorean Theorem. In using the squares, 10 was my Whole Number because it is the the closest perfect square before the number 117. I then got my Denominator by subtracting the two perfect squares from eachother. I got the numeratoe by subtracting the main number and the smaller perfect square. I couldn't end my answer with a Mixed fraction so I divided 17 to 21 to came up with a decimal form.

For the missing leg B I did the similar steps like the missing hypotenuse, but it changed when it came to the subtracting part. To get "B" you had to subtract A from C. After those steps you were back to the normal "missing side" steps.

For the missing leg A it was the same as Missing side B. The square is just in a different position during the subtracting steps.

Part 3:

Before I could do the Pythagorean Theorem, I first had to write down what I knew. The height of the frog from the tongue is 70 cm ( there is 100 cm in a m). The height of the door was 2m. And the distance from Lefrog and the door was 1.5 m. But I couldn't make a triangle just with that information. I had to find out what the height of the door is starting from the height of the tongue. So I had to subtract 70 from 200 which made 130cm or 1.3m. From there, I had my A (1.3) and my B (1.5). That's when I could use those numbers and the Pythagorean Theorem to solve the answer.

Part 4:

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Just in case you guys can't read the question. It says, " Mary had a dream to dunk. So one day she attempted. She stood at the free throw line, which was 20 feet away from the net. The basketball net's height is 10 feet tall. Mary is 4 feet tall for her feet to her arms. Her arms has a reach of 1 feet. How far and high does she have to jump to SLAM DUNK???

First you had to write down what you knew. After that you had to make the triangle with the starting lengths. I subtracted 4 from 10 to get the starting height(A). I subtracted 1 from 20 to get the starting distance(B). Once I got those facts, I could finally do the Pythagorean Theorem. After I get the number for C², I could use the squares and get the Mixed Fraction. After that, I would just have to divide the Numerator to the Denominator, and add the answer to the Whole Number.

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