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## Can you explain this please? Anyone?

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+ b= c2 (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 a2 + b2 = c → square root(a2 + b2) = square root(c2) → square root(a2 + b2) = c.

to find leg a, we isolate aand then square root both sides of the equation.

so a2 + b2 = c a= c- b2  → square root both sides and we get a= square root(c2 - b).

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

so we will get b= square root(c2 - a2).

PART TWO. (CIRCLES)

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

x+ y= r2.  and we know that

sinθ = y

cosθ = x

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

Assume angle θ

→ (cosθ)2 + (sinθ)= 1

Algebra and Geometry do not go into part TWO.

you are welcomed.

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!