What is the pthagorean thryum and what are its implications/aplications?

Question

This wouldld help greatly with my geometry. i dont really get what the pythagorean thyrum is.

Answer 1

The Pythagorean theorem involves a right triangle, its hypotenuse (c) and other two sides a and b. A right triangle is a triangle with one 90-degree angle. You can refer to a right angle as the corner of a piece of paper. The hypotenuse is the longest side of the triangle.

The Pythagorean theorem states that when c is the hypotenuse and a and b are the legs in a right triangle, then:

A squared + B squared = C squared

in other words...say you use the bottom corner of a piece of paper as your triangle.


|
|
|______

the line going up and down is 'a'
the line going across the bottom is 'b'



The slanted line from the end of the A line to the end of the B line is your hypotenuse. So the length of the 'a' line squared, plus the length of the 'b' line squared, is equal to the line that connects them 'c' squared.

Answer 2

The Pythagorean Theorem is used to find the unknown side of a right triangle. It goes like this: A^2+B^2=C^2. This means that the square of side A plus the square of side B will equal the square of side C. Here is an example: The measure of side A =3, and the measure of side B=4. 3^2=9, and 4^2=16. 9+16=25. The square root of 25 is 5, and so the measure of side C is equal to 5.

Answer 3

what all of your previous answerers failed to mention is that ANY 3 similar areas which have 3 sides which form a pythagorean triple have the pythagorean property of area as well!!

for instance suppose you had 3 semicircles with diameters 3, 4, 5
then area of circle with diameter 3 plus area of circle with diameter 4 equals area of circle with diameter 5

try a simpler example say 3 equilateral triangles with bases 3,4,5 and a common hieght say 1 see if the two triangular areas with bases 3 and 4 are equal to area of triangle with base 5

a^2+b^2=c^2 is just a special case of square areas

this is an often overlooked extension of theorem

as for applications i will give you one simple but powerful example

if a carpenter measures 3 feet from corner along one wall and 4 feet from same corner along second wall then the corner is a right angle as desired only if the tape when stretched from 3 foot end to 4 foot end diagonally reads 5 feet

see surveying, vector graphics for others

enjoy

Answer 4

The pathagorean theorm is: a (leg) squared + b (leg) squared = c(hypotenuse) squared. This is used for right triangles and their sides.

For example:
A right triangle has a leg of 3 cm and another leg of 4 cm.
3^2 + 4^2 = c^2
3*3 + 4*4 = c^2
9 + 16 = c^2
25 = c^2
squareroot of 25 = 5
so the hypotenuse is 5.

Answer 5

Pythagorean Theorem

Applies to a triangle

The formula is: c² = a² + b²

C² is the length of the Hypotenuse

a² is the length of the adjacent side

b² is the length of the opposite side