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Can you explain this please? Anyone?



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

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Kristina K. | A Tutor With Skills, Experience, Knowledge & PatienceA Tutor With Skills, Experience, Knowled...
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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
Paulo Y. | Math Tutor, SoccerMath Tutor, Soccer
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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

and r is the radius

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

Assume angle θ

→ (cosθ)2 + (sinθ)= 1 

 

 

 

Comments

Algebra and Geometry do not go into part TWO.

you are welcomed.

Christie W. | Reliable, Vibrant and Experienced TutorReliable, Vibrant and Experienced Tutor
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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!

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