Trigonometry – Right Angled Triangles By the end of this lesson you will be able to identify and calculate the following: 1. Who was Pythagoras 2. What.

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Presentation transcript:

Trigonometry – Right Angled Triangles By the end of this lesson you will be able to identify and calculate the following: 1. Who was Pythagoras 2. What is Pythagoras’ Theorem

 Pythagoras of Samos (born 580 BC, died 501BC) was a Greek Mathematician. Pythagorean theorem  He is best known for the Pythagorean theorem, which bears his name. He was known as "the father of numbers”. related to mathematics  Pythagoras believed that everything was related to mathematics and that numbers were the ultimate reality and, through mathematics, everything could be predicted and measured in rhythmic patterns or cycles.  Pythagoras once said that "number is the ruler of forms and ideas and the cause of gods and demons.”

right-angled triangles  Pythagoras’ Theorem involves looking the properties of right-angled triangles opposite  In any triangle, the longest side is opposite the largest angle opposite the right angle  So in a right-angled triangle, the longest side is opposite the right angle. hypotenuse  This side has a special name. It is called the hypotenuse.

 The theorem, or rule, named after him states that:  In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.  The rule is written as: c 2 = a 2 + b 2 ▪ Where, a and b are the two shorter sides, and, ▪ c is the hypotenuse.

 We are able to find the length of the hypotenuse when we are given the length of the two shorter sides by substituting into the formula c 2 = a 2 + b 2

 Worded problems can be solved by drawing a diagram and using Pythagoras’ theorem to solve the problem.  Worded problems should be given a worded answer.