Study various aspects of Pythagoras theoremplease i need its answer in 10 pages

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neela | High School Teacher | (Level 3) Valedictorian

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1  a and b  are adjascent sides of right angle and c is the hypotenuse. Then a^2+b^2 = c^2.

2. The sum of the area of the squares  formed by the right angle forming sides equal to the area formed of the square on the hupotenuse.

3. Given the length and breadth of any rectangle  we can find its hytenuse.

4 Given  any two sides of a right angled triangle we can find the 3rd side.

5.Given the length breadth and height of a cuboid (or a prism of rectangular top and bottom) , we can determine the diagonal.

6. The trigonometry and its developmement has its base on Pythagoras theorem.

7 The spherical trigometry and astronomy has its base on the Pythagoras theorem.

8.We can determine the height of a tree without climbing it. Using angle and known distance on the ground.

9 We can determine the distance between two objects in the sky with angles at different points on the ground without undergoing the difficulty of reaching the sky.

10. We can find the distance of a ship in the sea or between two ships in the sea without jumping into the sea.

12. You ca say whether a wall is perpendicular to the horizontal plane or ground.

14. You can form your own set to measure a right angle.

15. You can test whether a given angle is 90 degree or not.

16. It has enriched maths.

Use the idea and develop. There are a lot which you can think and write also.

Try the following link which may help for a K-9 student.

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publicspeaker | Student, Grade 11 | (Level 1) Honors

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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

The theorem can be written as the Pythagorean equation relating the lengths of the sides a, b and c :[1]

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. 

The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof,[5][6] although it is often argued that knowledge of the theorem predates him. (There is much evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they fitted it into a mathematical framework.[7]) “[To the Egyptians and Babylonians] mathematics provided practical tools in the form of "recipes" designed for specific calculations. Pythagoras, on the other hand, was one of the first to grasp numbers as abstract entities that exist in their own right.”[8] In addition to a separate section devoted to the history of Pythagoras' theorem, historical asides and sources are found in many of the other subsections.

The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power. The article ends with a section on pop references to the theorem.

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