How do you use Pyhagorean Theorm in math ?

Question

Its my first time I am and I am trying to learn it

Answer 1

It's easier if I (try) to draw it. :)

**Please ignore the little dots on the inside of the triangle; that's just so that it doesn't get all squished when I hit submit.**

|.\
|...\
|.... \
|.......\
|.........\
|*____\

^ That's supposed to be a right triangle.

Anyway, let's assume that the side all the way to the left is 4 inches long. We'll call that side "a." So, a = 4 inches, right?

Now, let's say that the base (the bottom side) is 3 inches long, and we'll call it "b." b = 3 inches

What the Pythagorean Theorum helps us do is find the third side (the diagonal one) which is called the HYPOTENUSE. The hypotenuse is always the side that is opposite of the right angle of the triangle, and it's always called "c" when used in an equation. See where side a and b meet (I put a little star there)? That's the right angle, so if we go across from that, we see side c, the hypotenuse. The formula for the Pythagorean Theorum is:

a^2 + b^2 = c^2

OR:

the length of the first side (remember we labled it a?) X itself + the length of the second side (labled b) X itself = the length of the hypotenuse (labled c) X itself

Let's try it with real values!

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

Now we have to work out the problem:

4^2 = 16
3^2 = 9

So, we have:

16 + 9 = c^2
25 = c^2

Since we can't have the value of the third side in squared form, how do we get c alone without the ^2? We find the square root of it. And remember, whatever you do to one side of the equation has to be done to the other, meaning that you have to find the square root of 25 as well.

We're left with

5 = c

The length of the third side (the hypotenuse) is 5 inches. :)

I hope this helps and have fun with geometry!!

Answer 2

You will see it written most often as a^2 + b^2 = c^2 where a, b, and c are the lengths of the side of a right triangle. a and b are the legs of the triangle and c is the hypotenuse.

Most often, you will be given two of the sides and be asked to compute the third side. So, let a = 3, b = 4 what is the length of the hypotenuse of this right triangle?

3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
5 = c (of course, as you know, there is also the negative when you extract a square root, so -5 is an answer as well, but it is difficult to imagine a triangle with a side that has a negative length.) So, you have found a right triangle with sides 3, 4, and 5. Cool.

Sometimes you will be give the hypotenuse and one leg and be asked to find the length of the other leg. So, suppose a = 5, c = 13, then what is b?

5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 169 - 25
b^2 = 144
b = 12

So now you have a right triangle with side 5, 12, and 13.

The most difficult are when the right triangle is isosceles, i.e., when the two legs are the same length --that's what you have to remember. So, you have an isosceles right triangle with one side of 3. What is the length of the hypotenuse?

3^2 + 3^2 = c^2
9 + 9 = c^2
18 = c^2
sqrt(18) = c
sqrt(9 x 2) = c
sqrt(9) x sqrt(2) = c
3 x sqrt(2) = c

The "tricky" question requires no calculation, but will show up on a test: you have an isosceles right triangle with one leg 7 and a hypotenuse of 7 x sqrt(2) what is the length of the other leg. I leave the answer as an exercise to the reader, but if you start to calculate this stop and *think*.

HTH

Charles

Answer 3

I thought it was, C^2 = A^2 + B^2

I don't know where the person got the extra variable 'A' onto the formula.

I thought that was a quadratic equation problem. But it has been a while since I did this kind of stuff.

I think all this theorem will allow you to do is find out what a particular side is, when giving two sides of a triangle.

Answer 4

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Answer 5

30 60 90 Triangle

view angle A , the 30° vertex

the side opposite the 30° vertex is called the opposite side
or side a

The side opposite the 60° vertex is called the adjacent side or side b


The side opposite the the 90° angle is called the hypotenuse side c


in order to caculate the length of one of the sides when two of the lengths are known. Pythagorean Tneorem is used.

c² = a² + b²

- - - - - - - - -s-

Answer 6

a^2 * b^2 = c^2

the three sides of a triangle are abc you know ab plug in to find c

Answer 7

if there is a right angled triangle
then (ac)^2=(ab)^2+(bc)^2