Pythagoras' Theorem. Please help me explain wat is this! I NEED HEEEEEEEEEELP!

Please help!

Pythagoras' Theorem. Please help me explain wat is this! I NEED HEEEEEEEEEELP!

Please help!

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The Pythagorean theorem, a^2+b^2=c^2, is used when you are given a right triangle (a triangle with one right angle) and you are asked to find either side a, b or c (given two sides). Sides a and b are the lengths of any two of the legs (long leg or short leg) and side c represents the length of the hypotenuse(the longest side of a right triangle).

The Pythagorean theorem is also used to prove whether or not you have a right triangle. For instance, if a^2+b^2 does not equal c^2, you do not have a right triangle. You may have an acute or obtuse triangle, instead. If a^2 +b^2>c^2, you have an acute triangle (a triangle with three acute angles)

for ie.) 55 degrees+ 60 degrees+65 degrees=180 degrees (the sum of the measures of all three angles in any triangle). 6625>4225

Moreover, if a^2 +b^2<c^2, you have an obtuse triangle (a triangle with only one obtuse angle)

for ie.) 35 degrees+50 degrees+95 degrees =180 degrees.

3725<9025

*a right angle measures exactly 90 degrees

*an acute angle measures less than 90 degrees

*an obtuse angle measures greater than 90 degrees

Pythagora's Theorem, better known as the Pythagorean Theorem, is a mathematical equation that relates the sides of a right angle triangle. I could also relate to so many other things.

TYPE ONE. (TRIANGLES)

It states that : a^{2 }+ b^{2 }= c^{2 (the sum of the squares of the legs = the square of the hypotenuse).}

where a and b are legs of the right angle triangle and c is the hypotenuse(the longest side).

It is normally used to find the sides of the triangle.

To find the hypotenuse, we simply square rot both sides of the theorem.

so a^{2} + b^{2} = c^{2 } → square root(a^{2} + b^{2}) = square root(c^{2}) → **square root(a ^{2} + b^{2}) = c.**

**
**to find leg a, we isolate a

so a^{2} + b^{2} = c^{2 }→^{ }a^{2 }= c^{2 }- b^{2} → square root both sides and we get
**a= square root(c**^{2} - b^{2 }**).**

**
**To find leg b, just interchange a and be the solve using the same procedure.

so we will get **b= square root(c ^{2} - a^{2}).**

PART TWO. (CIRCLES)

another way of representing the Pythagorean Theorem is by using it to relate to a circle.

x^{2 }+ y^{2 }= r2.^{ }and we know that

sinθ = y

cosθ = x

and r is the radius

so for a unit circle (radius = 1), we have

Assume angle θ

→ **(cosθ) ^{2} + (sinθ)^{2 }= 1 **

The Pythagorean Theorem is used when dealing with right triangles. It is used when determining the length of one side of a right triangle. In words it says that in any right angled triangle (one angle being 90°), the square of the hypotenuse is equal to the sum of the squares of both legs.

In equation terms it is written as a^2 + b^2 = c^2.

So if you are given the length of two of the sides you can determine the other side.

For example: If Side a = 3 and side b= 4 that means that c^2 = 32 + 42. c^2 = 9 + 16. c^2 = 25. C= .

So the length of side C=5, this is also known as the Hypotenuse.

Hope that helps!

Thank you!

Daisy C.

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## Comments

Algebra and Geometry do not go into part TWO.

Thanks man! For your tutorial!

you are welcomed.