... Then the biggest square has the specific same area together the various other two squares put together!


*

It is dubbed "Pythagoras" Theorem" and also can be composed in one brief equation:

a2 + b2 = c2

*

Note:

c
is the longest side of the triangle a and also b room the other two sides

Definition

The longest side of the triangle is referred to as the "hypotenuse", for this reason the formal an interpretation is:


In a right angled triangle:the square the the hypotenuse is same tothe sum of the squares of the various other two sides.

You are watching: A 2 b 2 c 2 solve for b


Example: A "3, 4, 5" triangle has actually a ideal angle in it.

*

Let"s check if the areas are the same:

32 + 42 = 52

Calculating this becomes:

9 + 16 = 25

It works ... Like Magic!


*

Why Is This Useful?

If we recognize the lengths that two sides that a appropriate angled triangle, we can find the size of the third side. (But mental it only works on appropriate angled triangles!)

How carry out I use it?

Write it down as one equation:


*
a2 + b2 = c2

Example: fix this triangle

*


*

Read Builder"s math to see practical uses because that this.

Also read about Squares and Square root to uncover out why √169 = 13


Example: resolve this triangle.

*


Example: What is the diagonal distance throughout a square of dimension 1?

*


It works the other way around, too: once the 3 sides that a triangle make a2 + b2 = c2, climate the triangle is ideal angled.


Example: does this triangle have a ideal Angle?

Does a2 + b2 = c2 ?

a2 + b2 = 102 + 242 = 100 + 576 = 676
c2 = 262 = 676

They room equal, for this reason ...

Yes, it does have a best Angle!


Example: go an 8, 15, 16 triangle have actually a right Angle?

Does 82 + 152 = 162 ?

82 + 152 = 64 + 225 = 289, however 162 = 256

So, NO, the does not have a appropriate Angle


Example: does this triangle have actually a ideal Angle?

*

Does a2 + b2 = c2 ?


And You deserve to Prove The Theorem yourself !

Get file pen and also scissors, then using the following animation as a guide:

attract a right angled triangle on the paper, leaving lot of of space. Draw a square along the hypotenuse (the longest side) attract the same sized square on the other side the the hypotenuse draw lines as shown on the animation, favor this:
*
cut out the shapes Arrange castle so that you have the right to prove that the big square has actually the same area together the 2 squares ~ above the various other sides

Another, Amazingly Simple, Proof

Here is one of the oldest proofs that the square ~ above the lengthy side has the very same area together the other squares.

Watch the animation, and pay attention once the triangles start sliding around.

You may want to clock the animation a few times to recognize what is happening.

The violet triangle is the necessary one.

See more: Is It Ok To Wire Light Switches And Lights With 12/2 Vs 14/2

*
becomes
*

We likewise have a proof by adding up the areas.


historic Note: while we contact it Pythagoras" Theorem, the was likewise known by Indian, Greek, Chinese and also Babylonian mathematicians well before he lived.
511,512,617,618, 1145, 1146, 1147, 2359, 2360, 2361
Activity: Pythagoras" TheoremActivity: A walk in the Desert
right Angled triangles The Fishing rod Pythagoras in 3D Pythagoras Generalizations triangle Pythagorean Triples Pythagorean theorem Algebra Proof