What is the Pythagorean theorem? How is it used?

Answer 1

A^2+B^2=C^2
Its used for calculating sides of a triangle but most commonly for calculating the hypotenuse...it can also be used to determine angles..among other things..

Answer 2

a squared+ b squared =c squared
it works on a right angled triangle to work out the missing lengthPythagoras' Theorem
Years ago, a man named Pythagoras found an amazing fact about triangles:



If the triangle had a right angle (90°) ...

... and you made a square on each of the three sides, then ...

... the biggest square had the exact same area as the other two squares put together!

The longest side of the triangle is called the "hypotenuse", so the formal definition is:

In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.


So, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²):

a2 + b2 = c2


Sure ... ?
Let's see if it really works using an example. A "3,4,5" triangle has a right angle in it, so the formula should work.


Let's check if the areas are the same:

32 + 42 = 52

Calculating this becomes:
9 + 16 = 25


yes, it works !

Why Is This Useful?
If we know the lengths of two sides of a right angled triangle, then Pythagoras' Theorem allows us to find the length of the third side. (But remember it only works on right angled triangles!)

How Do I Use it?
Write it down as an equation:
a2

Answer 3

The Pythagorean theorem shows a relationship between the three sides of a right triangle. If you know any two sides lengths you can calculate the third.

a² + b² = c²

where a and b are the two "legs" of the triangle and c is the hypotenuse.

Answer 4

"The square of the hypoteneuse of an isoceles triangle is equal to the sum of the square on the other two sides."

An isoceles triangle is on that has a right angle, which therefore creates a long side at odd angles to the other two legs. This is the hypoteneuse, and Pythagorus discovered how to determine the length thereof.

An example of why that is useful is in building a sloped roof. Since you know the width and height, you can use the Theorum to find the length of the beam required in advance, and also the area of the roof that will need covering. The effect of Pythagous' discovery on early Greek architecture (from which the Europeans learned to build) cannot be overstated.

Answer 5

a^2 +b^2 = c^2
it is used on triangles with three unequal sides(don't remember what it's called) and have a right angle. a and b are the two small sides and c is the hypotenuse (the largest side). So, for example, if the two smaller sides were 3 and 4, then 3 squared is nine and four squared is 16. add them together and you get 25, which is c^2. if you square root 25, you get five. This is the basic three four five triangle, used to teach this very thing.

Answer 6

a squared + b squared = c squared, the sum of the squares of the legs of a right triangle equals the square of the hypotenuse.

It’s really central to Trigonometry

Let the radius of a circle be C
and the Hypotenuse of a right triangle.

Let the sin of x be A/C
Let the cos of x be B/C

Then sin^2 x+cos^2x=
A^2/B^2 + C^2/B^2 =

(A^2+B^2)/C^2
But with Pathygoras
A^2 + B^2 = C^2
Replacing:
C^2/C^2 = 1
So we get the primary trigonometric identity:
Sin^2 * x + cos^2 * x = 1
Cool, yes?

Answer 7

a^2 + b^2 = c^2

It is used to determine the length of a side of a right triangle when two of the other lengths are already given.

Answer 8

All of the above comments are correct,you should refer to this website for further understanding.
http://www.themathpage.com/aTrig/pythagorean-theorem.htm

Answer 9

c^2=a^2+b^2
it is used to find the size of the perpendicular triangle, demanding the two sizes are already given.

Answer 10

a squared + b squared = c squared

it's used to make people remember the equation but forget what it's used for