46 lines
2.1 KiB
Markdown
46 lines
2.1 KiB
Markdown
---
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title: Pythagorean Theorem
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---
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## Pythagorean Theorem
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The Pythagorean Theorem relates the three sides of a right triangle. A right triangle is a triangle in which one of the angles is a right angle (a 90-degree angle). The side of the triangle that is opposite to the right angle is called hypotenuse. Any of the other two side can be named 'base'(b) and the 'perpendicular/height(a)'. The angle opposite to the base(b) is denoted by 'B' and the one opposite to perpendicular'A'. By this the angle C is 90 degrees and is known as a right triangle.
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A right triangle can only be isosceles or scalar. Never equilateral.
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Let c be the length of the hypotenuse, a and b the length of the other sides.
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The theorem states:
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c<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup>
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c = √(a<sup>2</sup> + b <sup>2</sup>), where c > 0
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Whenever you are given two sides of a right triangle, you can calculate the third one using the Pythagorean Theorem.
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In some instances, the value of the perpendicular height or the base may not be given, but the value of the hypotenuse can be given. So in this case:
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Let c become the length of the hypotenuse, a become the length of the perpendicular, and b become the length of the height. The Pythagoras Theorem is given by:
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a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup>
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The first case will be finding the unknown value of the perpendicular height, which is 'a'. So firstly, we will make a<sup>2</sup> become the subject:
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a<sup>2</sup> = c<sup>2</sup> - b<sup>2</sup>
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And then, we will square root both sides to get the value of a:
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a = √(c<sup>2</sup> - b<sup>2</sup>)
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For the second case, we will be finding the unknown value of the base, which is 'b'. So we will firstly make b<sup>2</sup> become the subject:
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b<sup>2</sup> = c<sup>2</sup> - a<sup>2</sup>
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And then, we will square root both sides to get the value of b:
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b = √(c<sup>2</sup> - a<sup>2</sup>)
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#### More Information:
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- <a href = "https://www.khanacademy.org/math/basic-geo/basic-geometry-pythagorean-theorem">Khan Academy Pythagorean Theorem</a>
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- <a href = "https://en.wikipedia.org/wiki/Pythagorean_theorem">Wikipedia Pythagorean Theorem</a>
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