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Finding the missing sides using Pythagorastheorem and trigonometry

ABSTRACTPythagoras theorem or trigonometric functions can be used to calculate the missing side or thesize of a right-angled triangle. Pythagoras Theorem and Trigonometric functions play a key rolein GCSE mathematics both in foundation and higher papers. It is important that the studentsunderstand the concept of the theorem to build further in Geometry. The basic aim of this paperto analyse that how Pythagoras and trigonometric theorem usually beneficial for real worldbecause there concept applied for the purpose of construction of building and also measure thedistance of mountain and rope. This paper is discussed about the issue related to thecontemporary pedagogy in this topic nowadays. In current scenario, Modern approach help forteach the meaning full concept and understand the idea that applied in the real world.

Table of ContentsABSTRACT.....................................................................................................................................2INTRODUCTION...........................................................................................................................4DISCUSSION..................................................................................................................................5LITERATURE REVIEW................................................................................................................9MISCONCEPTIONS.....................................................................................................................11CONCLUSION..............................................................................................................................17REFERENCES..............................................................................................................................18

INTRODUCTIONThe Pythagoras theorem is basically the fundamental relation with the Euclidean geometry thatconsists of three side of right triangle. The Pythagoras theorem plays an important role in themathematics and geometry. This theorem is beneficial for the two dimensional navigation andalso easily identify the shortest path and distance. This will be used in different areas and fieldsuch as mathematics, science, music etc. There is a long 4000 years of history behind thistheorem. Many researchers and great mathematicians had proved this theorem and embraced itsimportance in their work (Maor, 2007). According toPythagoras, It can be easily calculate theactual solution with the help of number and values. Mathematicis the basic foundation foreverything. Geometry is the highest form of mathematical studies to apply the new approach forthe measurement. The physical world could be understood through mathematics.He connectedthe patterns and contributed theories to understand the relations of angles, triangles, areas,proportion and polygons.

DISCUSSION“To this day, the Pythagoras’ theorem remains the most important single theorem in the whole ofmathematics” – Jacob Bronowski, (2017). The Ascent of Man, P160The Pythagorean Theorem is a cornerstone of mathematics and continues to be sointeresting to mathematicians that there are more than 400 different proofs of the theorem,including an original proof by President Garfield. In thisstudy and research carried out thenational curriculum and pedagogy of mathematics in schools all over the country andinternationally. The Pythagorean theorem is consists of various proofs:According to the right triangle, the length square of hypotenuse always equal to the sum ofanother side of triangle.a² + b² = c²Method- 1According to this triangle, It will be prove thata² + b² = c²First of all, it can be constructed the perpendicular from C to segment AB.Illustration1Illustration2

In this right triangle, The altitude is divided into the right angle to the hypotenuse in thedifferent two segments e and f. According to geometric, the length of each side of right triangleis the geometric means that the length of hypotenuse. On the other hand, the hypotenusesegments is the adjacent to the side.Therefore,c / a = a / e and c/ b = b / fStep 1: it is cross multiply in the both the sides and generate the ratio.ce = a^2cf= b^2Step 2: Add a and ba^2 + b^2 = ce+cfStep 3: Factoring out the c on the right side that given:a^2 + b^2 = c(e+f)Step: Substitutionc= e+fa² + b² = c²

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