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o-na [289]
3 years ago
14

What is the Pythagorean theorem and how do I use it?

Mathematics
2 answers:
SVETLANKA909090 [29]3 years ago
5 0
Pythagorean theorem that only works with right triangles! People use Pythagorean theorem to find the length of the hypotenuse of a right triangle if they know the length of the other two sides (legs)!

Including that people also use the Pythagorean theorem to know whether a triangle is a right triangle!

The equation used is :
a^2 + b^2 = c^2


Example :

Suppose that you have right triangle has a = 24 and b = 7

you square both

24^2 + 7^2

Then calculate

576 + 49

Add = 625

Then take the square root

Square root of 625 = 25^2

So the final answer would be
24^2 + 7^2 = 25^2


Hope this makes sense :)




Leviafan [203]3 years ago
4 0
I actually just learned this in 8th grade and it was so easy its crazy but its honestly simple it helps you solve the triangles and things and the equation is a squared + b squared = c squared and the a and b you would plug in the sides of the triangle or whatever shape your working with and square those numbers then find c by adding the two and then you square the c at the end and that will be your answer.

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The endpoints of a line segment AR are A(8,-2) and R(-4,1). What is the length of the AR?
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Answer:

The length of the AR is  3\sqrt{17}  or 12.4 units.

Step-by-step explanation:

Given the endpoints of a line segment AR

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  • R(-4, 1)

We can calculate the length of AR using the formula

L_{AB}=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

In our case,

  • (x₁, y₁) = (8, -2)  
  • (x₂, y₂) = (-4, 1)

Substituting (x₁, y₁) = (8, -2) and (x₂, y₂) = (-4, 1) in the formula

L_{AB}=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

        =\sqrt{\left(-4-8\right)^2+\left(1-\left(-2\right)\right)^2}

        =\sqrt{\left(-4-8\right)^2+\left(1+2\right)^2}            ∵ Apply rule:  -\left(-a\right)=a

        =\sqrt{12^2+3^2}

        =\sqrt{144+9}

        =\sqrt{153}

        =\sqrt{9\times 17}

         =\sqrt{17}\sqrt{3^2}          Apply radical rule:   \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}

         =3\sqrt{17}              Apply radical rule:   \sqrt[n]{a^n}=a

         =12.4

Therefore, the length of the AR is  3\sqrt{17}  or 12.4 units.

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