The Pythagorean Theorem
Almost 2,500 years ago, Pythagoras, a Greek mathematician, discovered a relationship that exists between the length of the hypotenuse of a right triangle and the legs of the triangle. A right triangle is any triangle that has a 90 degree angle It has two legs and a hypotenuse. The legs will always be labeled a and b and the hypotenuse is always labeled c. The hypotenuse is always the longest side of a right triangle; the side opposite the right angle
The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. This is written \( a^2+b^2=c^2\). Because of this relationship, if we know that a = 3, and b = 4, we can solve for c.
Step 1: Gather the facts. In this case, we know that he legs of the right triangle measure 3 and 4.
Step 2: Since this is a right triangle, we can use the Pythagorean Theorem to find c.
\({a^2} + {b^2} = {c^2}\\{3^2} + {4^2} = {c^2}\\9 + 16 = {c^2}\\25 = {c^2}\)
\(c = \sqrt {25} \)
Step 3: The variable c is equal to the square root of 25. If you need to, you can use a calculator to find the value of \(\sqrt {25} \). Enter the number 25 and then press the \(\sqrt {\;\;} \) symbol.
Answer: c = 5
