


Pythagorean Theorem
Name of the sides in Right TriangleThe side AC is called the hypotenuse of the right triangle. The side which is opposite to 90 degree is called the hypotenuse side and it is the longest side and is opposite to the right angle. Greek mathematician Pythagoras has found that the length of the square on the hypotenuse is equal to the sum of the length of the squares on the other two sides. That is AC ^{2} = AB ^{2} + BC ^{2}. This is knows as Pythagoras theorem. The PythagoreanTheorem is the most famous mathematical contribution.The later discovery that the square root of 2 is irrational and therefore, that cannot be expressed as a ratio of two integers, extremely troubled Pythagoras and his followers. They were consume in their belief that any two lengths were integral multiples of some unit length. Many efforts were made to suppress the knowledge that the square root of 2 is irrational.
Pythagorean TheoremExample problems
AB= 5 cm , BC = 12 cm we know AC ^{ 2} = AB ^{ 2} + BC ^{ 2} AC ^{ 2} = 5^{ 2} + 12 ^{2}
2. Find the length of the missing side.Here angle C is 90°. AB = √5 cm , AC = 1 cm By using Pythagoras theorem AB ^{ 2} = AC ^{ 2} + BC ^{ 2} 3.In a right triangle ABC right angled at C then AB = √7 cm , AC = 2 cm find BC. By using Pythagoras theorem AB ^{ 2} = AC ^{ 2} + BC ^{ 2} 
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