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STRIVE FOR EXCELLENCE TUTORING www.StriveForExcellence.com.au Pythagoras’ Theorem In relation to Mathematics, Pythagoras’ theorem is the relation of the three sides of a rightangled triangle. The theorem can be expressed as the equation below, and relates to the lengths of the sides of the triangle. c2=a2+b2 c a “a” & “b” are the 2 shorter sides and “c” is the Hypotenuse (longest side) b Pythagoras’ theorem can also be rearranged to find a shorter side. For example: a2 = c2-b2 Example 1: or b2 = c2-a2 For the triangle below, calculate the length of the Hypotenuse, x, correct to 1 decimal place. Step 1: Label the sides: a=4, b=7, c=x x 4 Step 2: Substitute the values in Pythagoras’ Theorem: c2 = a2 + b2 x2 =4 2 + 72 x2=16 + 49 x = 65 = 8.1 Example 2: 7 You can also use Pythagoras’ Theorem to work out if a triangle has a right angle Step 1: Does c2 = a2 + b2? 25 24 Step 2: 252 = 72+242 = 625 = 49 + 576 Step 3: 252 = 625 7 Both sides of the equation are equal so it is definitely a right angle triangle! © Copyright Strive for Excellence Tutoring 2012 STRIVE FOR EXCELLENCE TUTORING Pythagorean Triads On certain occasions, all 3 sides of a right angled triangle will be whole numbers. This is called a Pythagorean Triad (also called a Pythagorean Triple). The right angled triangle below is an example of a Pythagorean Triad. 5 4 3 We can use the following formula to create a Pythagorean Triad. Firstly, we need to find the middle number “m” of a Pythagorean Triad, where “s” is an odd number. The third number can then be found using Pythagoras Theorum. m= s2 −1 2 Example 3: How to create a Pythagorean Triad Step 1: Choose any odd number for your “s” value and then square it. We will choose “72 = 49” for this example. Step 2: Find 2 consecutive numbers that add up to the squared value in step 1. 24 + 25 = 49 If you have trouble doing this in your head, then use the formula mentioned above. 72 −1 Enter 7 into the equation: m = 2 Step 3: We end up with m = 24. Step 4: Write down the number you squared in step 1 and the 2 numbers from step 2. You now have your triple. 7, 24, 25 You can use Pythagoras to check the result. c2=a2+b2 252=242 + 72 625 = 576 + 49 25 7 24 © Copyright Strive for Excellence Tutoring 2012