PythagoreanTheorem

The PythagoreanTheorem is attributed to the Greek philosopher and mathematician Pythagoras who lived in the 6th century B.C. The theorem states a relationship between the lengths of the sides of a right triangle. It says:

The sum of the squares of the length the sides of a right triangle is equal to the square

of the length of the hypotenuse.

Visually, the theorem can be illustrated as follows:

Given a right triangle, with sides a and b and hypotenuse c, (Figure 1)

/ l

/ l

c / l

/ l

/ l b

/ l

/_____________l

a

Figure 1

the hypotenuse is the side opposite the right (90 degree) angle in a right triangle.

Then, c^2 = a^2 + b^2, or c = sqrt(a^2 + b^2).

Certain sets of 3 integers are useful to remember as being Pythagorean triples, that is,

they are possible lengths of the sides of a right triangle. For example:

a b c

3 4 5

9 12 15

The PythagoreanTheorem is an important tool in the study of TrigonometricFunctions.