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,
pythagorean-image
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,
c2 = a2 + b2
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
c2 = a2 + b2
c2 = 32 + 42
c2= 9 + 16
c2 = 25
c = √25
The sign (√) means square root
c = 5
Exercises #2 Let c = 10 and a = 8. Find b, or the other leg.
c2 = a2 + b2
102 = 82 + b2
100 = 64 + b2
100 - 64 = 64 - 64 + b2 (minus 64 from both sides to isolate b2 )
36 = 0 + b2
36 = b2
b = √36 = 6
Let c = 13 and b = 5. Find a
c2 = a 2+ b2
132 = a2 + 52
169 = a2 + 25
169 - 25 = a2 + 25-25
144 = a2 + 0
144 = a2
a = √144 = 12
Category:Math tips
Category:Proofs in geometry
Category:Pythagorean Theorem