what can u say about the pythagorean theorem"?

Question

article about pythagorean theorem

Answer 1

The squares of both sides added together equals to the square of the hypotenuse.

Which means the base squared plus the height squared equal to the hypotenuse squared

Anotther way to say it is the run squared plus the raise squared equals the hypotenuse.
Where the run is the base of the triangle distance measured from edge of the building to the center line of the roof (peak of the roof)
Where the raise is the height of the triangle is the height of the attic measured from the top of the ceiling to the top of the roof.
Where the hypotenuse of the triangle is the roof of the building.

In Electrical and electronics it is stated the resistance squared plus the reactance squared equals to the impedence squared.
Where: base of the triangle is the pure resistance
Where hieight of the triangl is the reactance
Where the hypotenuse of the triangle is the impedence.

To find the hypotenuse of a traingle add the base squared to the height squared which will equal the hypotenuse squared. Then take the square root of the hypotenuse squared:

Base of the triangel A. = 20 feet
height of the triange B = 15 feet
hypotenuse of the triangle C = ?

C^2 = A^2 + B^2

C^2 = 20^2 + 15^2

C^2 = 400 + 225
C^2 = 625
now take square root of both sides:

Square root of C = square root of 625

C = 25 ft. = hypotenuse of the triangle.

You can also find either side if you know the hypotenuse and one side you can find the other side:

A = base
B = hieght
C.= hypotenuse

it the base and hypotenuse are known find the height:

C^2= A^2 + B^2
use the additive inverse to get the height on one side of the equation and, get the hypotenuse and base on the other side of the equation.

C^2 - A^2 = A^2 + B^2 - A^2

C^2 - A^2 = B^2

To solve for the height subtract (take additive inverse) A^2 from C^2 then take the square roots of both sides of the equation:

If the base of a triangle is 20 and the hypotenuse of a triangle is 25 find the height of the triangle.

B = height
A = base
C = hypotenuse;

set it in standard form:

C^2 = A^2 + B^2
now take add the additive inverse of A^2 to both sides.(that means subtract A^2 from both sides of the equation

C^2 - A^2 = A^2 + B^2 - A^2

C^2 - A^2 = B^2
now plug in your numbers:

25 squared minus 20 squared equals B^2

625 - 400 = B^2

225 = B^2
now take square roots of both sides of the equation

sqaure root of 225 = square root of B^2

15 = B height of triangle is 15 ft.

I worked it one time keepin my unknown on left side of the equation:
Second problem I kept it on the right side. mainly to show it makes no difference which side of the equation sign you keep your unknown on while working the problem.

Personally I prefer keeping my unknowns on left side of the equation. That is more a personal preference than anything. Which ever you feel most comfortable with.
That is a long as you remember in your final answer to write it in the standard form with the unknown on the left side of the equation sign.

I never carried which side as long as my students got the equation right and showed their work. But some instructors did:

Hope that helps

Answer 2

Widely acknowledged to have been observed by Pythagoras...but it was most likely his followers who penned it (he had a religion/cult which essentially believed that everything is made of numbers [the arche, but that's philsophy]).

We all know the equation...a^2 + b^2 = c^2

But what it's saying is that the square root of the two shorter sides of a triangle are equivalent to the square root of the measure of the hypotenuse (longest side). There is actually a lot of reasoning behind this, but nobody really observes that...we just tend to plug in the numbers.

Answer 3

A man back in the ancient times took three sides of a triangle and said side A^2 + side B^2 = side C^2

Answer 4

a^2+b^2=C^2

basic if you ask me

Answer 5

http://www.arcytech.org/java/pythagoras/
http://jwilson.coe.uga.edu/EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html
http://www.cut-the-knot.org/pythagoras/index.shtml
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