Pythagorean theorem
The Pythagorean Theorem was named after famous Greek mathematician Pythagoras.
It is an important formula that states the following:
In any right triangle,
Let c be the length of the longest side, called hypotenuse
Let a and b be the length of the other two sides, called legs
The theorem states that the length of the hypotenuse squared is equal to the length of side a squared and the length of side b squared
Written as an equation,
c
^{2} = a
^{2} + b
^{2}
Thus, given two sides, the third side can be found using the formula
We will illustrate with examples
Before proceeding, you should know How to find the
square root of a number and how to
solve equations using subtraction
Exercises #1
Let a = 3 and b = 4. Find c, or the longest side
c
^{2} = a
^{2} + b
^{2}
c
^{2} = 3
^{2} + 4
^{2}
c
^{2}= 9 + 16
c
^{2} = 25
c = √25
The sign (√) means square root
c = 5
Exercises #2
Let c = 10 and a = 8. Find b, or the other leg.
c
^{2} = a
^{2} + b
^{2}
10
^{2} = 8
^{2} + b
^{2}
100 = 64 + b
^{2}
100  64 = 64  64 + b
^{2} (minus 64 from both sides to isolate b
^{2} )
36 = 0 + b
^{2}
36 = b
^{2}
b = √36 = 6
Let c = 13 and b = 5. Find a
c
^{2} = a
^{2}+ b
^{2}
13
^{2} = a
^{2} + 5
^{2}
169 = a
^{2} + 25
169  25 = a
^{2} + 2525
144 = a
^{2} + 0
144 = a
^{2}
a = √144 = 12
Take the Pythagorean theorem quiz below to see how well you understand this lesson.
Buy a comprehensive geometric formulas ebook. All geometric formulas are explained with well selected word problems.



Sep 18, 19 01:16 PM
Factoring using the box method. Common pitfalls to avoid when using this method.
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.