Pythagorean theoremThe Pythagorean Theorem was named after famous Greek mathematician Pythagoras In any right triangle, Let c be the length of the longest side, called hypotenuse Let a and b be the length of the other two sides, called legs The theorem states that the length of the hypotenuse squared is equal to the length of side a squared and the length of side b squared Written as an equation, c2 = a^{2} + b^{2} Thus, given two sides, the third side can be found using the formula We will illustrate with examples Before proceeding, you should know How to find the square root of a number and how to solve equations using subtraction Exercises #1 Let a = 3 and b = 4. Find c, or the longest side c^{2} = a^{2} + b^{2} c^{2} = 3^{2} + 4^{2} c^{2}= 9 + 16 c^{2} = 25 c = √25 The sign (√) means square root c = 5 Exercises #2 Let c = 10 and a = 8. Find b, or the other leg. c^{2} = a^{2} + b^{2} 10^{2} = 8^{2} + b^{2} 100 = 64 + b^{2} 100  64 = 64  64 + b^{2} (minus 64 from both sides to isolate b^{2} ) 36 = 0 + b^{2} 36 = b^{2} b = √36 = 6 Let c = 13 and b = 5. Find a c^{2} = a ^{2}+ b^{2} 13^{2} = a^{2} + 5^{2} 169 = a^{2} + 25 169  25 = a^{2} + 2525 144 = a^{2} + 0 144 = a^{2} a = √144 = 12 Buy a comprehensive geometric formulas ebook. All geometric formulas are explained with well selected word problems Need a Quick Answer to your Math Problems? Get an answer in 10 minutes or less from a math expert! Justanswer is 100% RISK FREE.You Pay Only for the Answers You Like. Fees are Typically $9$15
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