The Pythagorean Theory :

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