application of pythagoras theorem in daily life
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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.
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).
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!