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.
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