About 2500 years ago, a Greek mathematician Pythagoras found a revolutionary fact in a right triangle. He observed that in any right triangle,
Square of the measure of the hypotenuse = Sum of the squares of the measure of the legs.
This is one of the most famous theorems in mathematics help and named as Pythagoras theorem or Pythagorean theorem.
Pythagoras theorem has a wide applications in many field till today and would continue to have for ever.
Pythagoras Theorem
Look at the following diagram.
The Pythagoras theorem states that,
AB2 + BC2 = AC2
While the are so many methods to prove Pythagoras theorem, the following is a simple method.
From B, draw a perpendicular BD on AC.
It is clear that angle A and angle DBC are both equal to 90o – angle C
Therefore, the triangles ABD and ABC are similar and also the triangles BCD and ABC are similar.
Using the properties of similar triangles,
AB/AC = AD/AB and BC/AC = DC /BC
or, AB2 = (AD)(AC) and BC2 = (DC)(AC)
or, AB2 + BC2 = (AD)(AC) + (DC)(AC) = (AC)(AD + DC) = (AC)(AC) = AC2
Application of Right Triangle – Pythagoras Theorem
As mentioned earlier there are wide application of right triangles with the help of Pythagoras theorem.
The fundamental concept of the subject trigonometry is based on the right triangle and Pythagoras theorem. The trigonometric ratios are all based on right triangles. It is because of Pythagoras theorem, the identity sin2x + cos2x = 1 is established.
The geometrical representation of Pythagoras theorem helps in identification of irrational number.
math homework example, to construct a line of measure ?13 units draw a line segments of 2 units and 3 units perpendicular to each other with a common end points. The line segment joining the other endpoint will have the measure of ?13 units.
The application of right triangles and Pythagoras theorem have helped in proving a number of theorems and in solving countless problems in geometry. For example, the cosine rule and sine rule are derived from this concept. The equation of a circle is also framed that way.
Practical Application of Right Triangle – Pythagoras Theorem
The application of right triangles and Pythagoras theorem is a boon in many real situations. The distance between two places, measurement of heights and distances, resultants of two forces are a few of the examples.
All these applications are illustrated through various examples.
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