Pythagorean Theorem
How to find the side of a right triangle by using the Pythagorean theorem: formula, 2 examples, and their solutions.
Formula
Formula
The Pythagorean theorem (Pythagoras' theorem)
shows the relationship
between the sides of a right triangle.
a2 + b2 = c2
a, b: Legs
c: Hypotenuse
Example 1
Example
Solution
The legs are 4 and 3.
The hypotenuse is x.
So, by the Pythagorean theorem,
x2 = 42 + 32.
42 = 16
32 = 9
16 + 9 = 25
Square root both sides.
Then x = √25.
x is the lenght of the hypotenuse.
So x is plus.
So you don't have to write ± sign.
Quadratic Equation: Square Root
25 = 52
√52 = 5
Simplify a Radical
So x = 5.
Example 2
Example
Solution
The legs are x and 5.
The hypotenuse is √89.
So, by the Pythagorean theorem,
x2 + 52 + (√89)2.
+52 = +25
(√89)2 = 89
Move +25 to the right side.
Then x2 = 64.
Square root both sides.
Then x = √64.
x is the lenght of the leg.
So x is plus.
So you don't have to write ± sign.
64 = 82
√82 = 8
So x = 8.