The Pythagorean Theorem

Learn how to use it !

The Greek mathematician Pythagoras presented this simple (but still very useful) theorem. In the article you will learn about the theorem and how to use it correctly.
The Pythagorean Theorem states, the square of the hypotenuse c, is equal to the sum of the squares of the other two sides, which can be written as:

a2 + b2 = c2

TriangleCredit: ThomasNissenCredit: ThomasNissen

The image above shows a right-angled triangle. We indicate the sides with a small letter, and the angels with big letters. The side lying opposite for the angel B is the side b and so on. The right-angel is always named C, so the longest side in the triangle is c.

It is very important to remember that the theorem only applies to right-angled triangles! To find lengths and angels in a non-right-angle triangle we have to use trigonometry, which I will cover in another topic.

Now let’s see some examples:

Example #1:

We know that the length of a = 4 and the length of b = 3, then we can find the length of the hypotenuse c:

  • Put the value of a and b into the equation.

42 + 32 = c2

  • Evaluate the squares.

162 + 92 = c2

  • Add the two numbers together.

25 = c2

  • Find c by taking the root on both sides.

c =  = 5

And we are done, simple and easy.


Example #2:

We know that the length of a = 8 and the length of c = 12, then we can find the length of b:

  • Now that we want to find b, and not c we have to isolate b in the equation. We can do this by subtract “a2” on both sides of the equation:

b2 = c2 - a2

  • Put the value of a and c into the equation.

b2 = 122 - 82

  • Evaluate the squares.

b2 = 144 - 64

  • subtract 64 from 144.

b2 = 80

  • Find b by taking the root on both sides.

b = √80 = 8.94


So now you have learned to use the Pythagorean Theorem, and you can now find lengths in a right-angled triangle if you know the length of two of the sides. If you have any problems solving an equation using the Pythagorean theorem , or if you want more information about another mathematical topic please leave a message.