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# Applications Of Pythagoras Theorem In Daily Life

Pythagorean Theorem Introduction: Pythagorean Theorem  is invented by a Greek mathematician named Pythagoras from southern-Italy. He is the first mathematician to use his theorem to understand the real time application in day to day life. The theorem gives the relation between three triangle in Euclidean Geometry, which gives the formula to find length of the sides of any right triangle.

Maths Pythagorean Theorem: In any triangle the square on its largest side is equal to the sum of the squares on the reaming two sides. The triangle is right angled triangle and the angle opp to the largest side of the given triangle is called as hypotenuse of the triangle. The equation of  Pythagorean Theorem is given as a2 = b+ c2  which relates the length of the sides of the given three triangles.

Fig a: Three combined triangles

Applications of Pythagoras theorem: Application of Pythagorean theorem  are used in daily life like  to determine the slope of the triangle, in buildings. trajectory of a bullet,building fences,Navigation, GPS,Oscilloscopes,Mechanical Engineering calculation,Design engineering,Architecture Polar coordinates,Trigonometry, used in math for oceanography and Calculus. The application of the right angled triangle, especially the 3-4-5 triangle have been proved from vast years in the subject of mathematics.The Pythagorean Theorem can be used with any shape and for any formula that squares a number.  The Pythagorean Theorem only applies to right triangles. Since this triangle has a right angle, the sum of the squares of the other two sides can be used to find r.

Proof of Applications of Pythagoras theorem are given below

1.  To find the distance between the two given points:
A car travels 20 km from west to east. Then it turns left and travels a further 15 km. Find the displacement between the starting        point and the destination point of the car

Fig b : Direction of the Car

Solution by using  Pythagorean Theorem.
AC2 = AB2 + BC2
AC2 = 202 + 152
AC2 = 625
AC = 25

2. Determine whether given triangle is a right triangle.

Let us assume the sides of the triangle as √41,4,5.√41 be the longest side of the given triangle.

Fig c :Right triangle
AB2 = AC2 + BC2

( √41)2  = 4+ 52
( √41)2  = 16 + 25
41  = 41

Since LHS is equal to RHS, the triangle is a right triangle.

Question:I have to do a maths research project. I need to write about the history, Human use, Natural occurrences and about the Famous Mathmatician, Any help? Thanks.

Answers:The Pythagorean theorem states that the square on the hypotenuse of a right triangle has an area equal of the sum of squares of the other two sides. The Pythagorean theorem was a mathematical fact that the Babylonians knew and used. A triangle with sides a, b, and c (longest) is a right triangle if and only if a + b = c . Hence we know how the sides are related if is a right triangle. Common Pythagorean triple are: 3, 4, 5 5, 12, 13 7, 24, 25 9, 40, 41 and 6, 8, 10 All but the last triple are primitive, the last is called a multiple. A regular polygon has all sides equilateral and all angles equiangular. In a triangle, these cannot occur independently. The resulting triangle with sides in the ratio 1:1:1 and angles 60 -60 -60 is discussed. The three most important right triangles are: 3-4-5, the isosceles right (45 -45 -90 ), and 30 -60 -90 triangle. 3-4-5 triangle has angle measure of about 37 -53 -90 . Watch especially for these special angles and triangles. The isosceles (2 or more sides equal) right triangle can be thought of as having legs (the shorter side of a right triangle) of 1. Thus the hypotenuse is square root of 2. The 30 -60 -90 triangle can thought as a bisected equilateral triangle. Thus one side might be 1, hypotenuse then is 2 and the other side by square root of 3. These side length ratio must be memorized and will be seen often in trigonometry which is the study of triangle, but primarily involved triangle sides length ratio. Note: if a + b < c , the triangle is obtuse; if a + b > c , the triangle is acute. The most important application of Pythagorean theorem is for finding the distance between points in a plane. Distance = [ (x - x ) + (y - y ) ] With the above formula, Pythagoras (and other famous mathematicians) is able to create more formulae, each suitable for its purposes. Pythagoras's Identities: sin x + cos x = 1, tan x + 1 = sec x, cot x + 1 = cosec x Sine rule: a/sinA = b/sinB = c/sinB Cosine rule: a = b + c - 2bc cosA, b = a + c - 2ac cosB, c = a + b - 2ab cosC Heron's formula: A = [ s(s - a)(s - b)(s - c) ] Pythagoras was a great Greek philosopher responsible for important development in mathematics, astronomy, and the theory of matter. He left Samos because of the tyrant who ruled there and went to southern Italy about 532 BC. He founded a philosophical and religious school in Croton that had many followers. Of his actual work nothing is known. His school practiced secrecy and communal-ism making it hard to distinguish between the work of Pythagoras and of his followers. His school made outstanding contribution to the foundation in mathematics.

Answers:3D geometry explains different object with three-dimensional shapes, that cannot be sketched on papers. Spheres, Cones are the example of 3D. A ball is used in daily life. Motor car tyres are cylindrical and are also in daily use. You look at your TV which is a 3D object of daily use. A die is in the shape of a cube. A portable DVD player is in the shape of a rectangular prism.

Question:TESTS: a. putting NaOH solution and nitric acid-PROTEINS b. putting iodine solution-STARCH c. rubbing fats on a paper-FATS

Answers:(A) Police forensics units use this one to 'develop' fingerprints in certain circumstances. (B) Outside of a general biology lab, I cannot imagine any practical use in daily life. A sort of reverse version has been used as a medical test for sweating. An iodine solution is applied to the skin and allowed to dry, then dusted with starch. Since the reaction requires water, the treated skin will turn purple-black if/when sweating occurs. (C) The pioneers and other non-technology peoples used to make translucent window coverings by rubbing fats into thin animal skins. This allowed them to keep out the cold winds while letting in some daylight. I suppose there might be some similar application for paper, but I can't think of one (aside from maybe using it as a fire starter; fat-soaked paper would burn pretty easily).

Question:i'm making my term paper..and i badly need ur ans. thanks!

Answers:Clinical? Not sure about clinical....but in day to day life for sure.....eg Mining, to dissolves rock around gold, Vinegar, Bleaches, Agents such as bathroom mold removing products, Citric Acids used in cooking...the list is abundant!