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,

c2 = a² + b²

Thus, given two sides, the third side can be found using the formula

We will illustrate with examples

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