1. Pythagoras

1. Pythagoras

1. Pythagorean Triples

   • A Pythagorean triple consists of three numbers that all follow the formula a² + b² = c².
     • A common example of this are the numbers 3, 4 and 5, 3²=9, 4²=16 and 9+16=25 which is 5².

2. Finding The Hypotenuse

   • The longest side of a right angled triangle is called the hypotenuse and is always opposite the right angle.
     • a² + b² = c², in this formula c is the hypotenuse, so the sum of the squares of the two other sides is equal to the square of the hypotenuse
       • For example if a=12 and b=7: 12² + 7² = c² so, 144+49= c², 193 = c², √193 = c, so c = 13.9 (1 d.p).

3. Finding Any Side

   • Pythagoras can also be used to calculate any other side of the right angled triangle (a+b)
     • We can just swap the formula around to work out the other sides, c² - a² = b² or c² - b² = a².
       • For example if c=15 and b=4: 15² - 4² = 209 (a²) so √209 = 14.5 (1 d.p).