Pythagorean theorem

Pythagorean Theorem Report

By: Jessieca

8 Arctic

A.     Background

The Pythagorean theorem is important; because it will be apply on the daily life and also we will need this in jobs, works and other until were old (maybe). This is really important to us. It will be useful for jobs and other. There are some of examples where we need to learn Pythagorean, start from architecture, playing football and other. We can find Pythagorean everywhere. I will explain more about it in this report.

B.     Content

a.     What is Pythagorean theorem?

Before we learn more about Pythagorean theorem, we need to know what is Pythagorean theorem. Pythagorean theorem is the statement of right angle triangles, the Pythagorean theorem state that:

"The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."

Resource: http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.html

Picture from: http://www.mathwarehouse.com/geometry/triangles/images/right-triangles/the-pythagorean-theorem/pythagorean-theorem-picture.png

b.     Proving Pythagorean theorem

To use the Pythagorean theorem, we need to prove if it works or not. There are many ways to prove the Pythagorean theorem. So, one of the way is to make what it shown in the picture:

Picture from: http://www.mathsisfun.com/geometry/images/pythagorean-theorem- proof.png
In that picture shows a square in side a square, and form 4 right angles. This is how to prove it:

            (²= 2ab+ c²

We also need to consider about this calculation (a+b)(a+b), this calculation come from the area of the big circle.

2ab+c²=(a+b)(a+b)

2ab+c²= a²+ab+ba+b²

2ab +c²=a²+2ab+b²

c²=a²+b²

This is how does the Pythagorean theorem proved. They are actually more ways but this is the obvious way to prove it.

c.      Pythagorean theorem in real life.

Let’s start from the right angle triangles. We can find them everywhere. Start from things in our home to the environment. Like example, TV, Pillows, AC, field, or even everything that have square, rectangle or straight up right angled triangles. These are some example of Pythagorean, and the world problem.

1.     Road trips

There are 2 Friend, 1 of them is in the market and he asks him to come to the market also. He wants to find the shortest way. There are 2 paths he could go to. The first path is to heading west 1mile and heading south 4 miles, the total distance is 5 miles. The other way is just pass the other road. What is the difference of both of the roads?

To find the difference, we need to know the distance of the other road

We will use the Pythagorean theorem

1²+4²=c²

1+16=c²

= c

4,5=c

5 -4,5=0,5 miles

The differences is 0,5 miles

2.     TV size

One day Mari wanted to buy a TV. She goes to the shop and saw a big TV, but they do not mention how many inches is that TV. It only says have a height of 15 inches height and 20 inches wide. How many inches is the TV?

To find how many inches is the TV is to use the Pythagorean theorem.

15²+20²=c²

225+400=c²

=c

25=c

The TV is 25 inches big

Those are some examples of Pythagorean theorem. There are many of other examples, but these are only some of them.

Resources: http://www.brighthubeducation.com/homework-math-help/36639-applications-of-pythagoras-theorem-in-real-life/

C.     Conclusion

My conclusion about Pythagorean theorem is that Pythagorean theorem is really important. It is useful for jobs, it is also useful in real life. The Pythagorean can be applied really easily and it has an easily to remembered formula.