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.
Poser: (3,4,5) is a pythagorean triplet since 3^2 + 4^2 = 5^2. Which positive integers are not part of a pythagorean triplet?