How to Calculate the Pythagoras Theorem

The Pythagoras Theorem Explained!

Pythagoras might seem like an odd word to some. Do not let the letters confuse you, it’s a simple theorem, easy to understand!

This is a theory that was attributed to a man named Pythagoras and he had a theory that: The square root of the hypotenuse of a right-angled triangle is directly equal to the area of the sum on the adjacent sides. This theorem, therefore, can be written as     $A^{2}+B^{2}=C^{2}$

“The theorem has been given numerous proofs – possibly the most for any mathematical theorem. They are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed, to objects that are not triangles at all, but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps and cartoons abound.” – Wikipedia

This theorem is often used in mathematics. Understanding this theorem and getting it right is one of the fundamental mathematical exercises. This theorem is used right through high school and is tested even in matric.

Let us start off with a simple example to help us understand the theorem.

Example 1

Following the Pythagorean theorem, we need to follow the formula given to get the correct answer to our equation namely $A^{2}+B^{2}=C^{2}$

$A^{2}+B^{2}=C^{2}$        Use the formula given.

$4^{2}+3^{2&space;}=&space;C^{2}$        Replace the A value and B values with the numbers given.

$16+9&space;=&space;C^{2}$          Simply the equation further.

$C^{2}=25$

$\sqrt{C^{2}}=\sqrt{25}$

$C=5$

The formula has algebraic proof in that it can be used to work out the side of the triangle if we have the hypotenuse value.  Let us consider another example using the same triangle.

Example 2

Consider the same triangle below.

$A^{2}+B^{2}=C^{2}$

$4^{2}+&space;B^{2}=&space;5^{2}$   Notice that we have the values for A and C

$B^{2}=&space;5^{2}-4^{2}$   Arrange the values to determine B

$B^{2}=&space;25-16$   Simplify the equation further

$B^{2}=&space;9$

$\sqrt{B^{2}}=\sqrt{9}$

$B=3$

To show our findings and test out the theory, let us look at our last example…

Example 3

Consider the same triangle below.

Again we need to begin using our formula.

$A^{2}+B^{2}=C^{2}$

$A^{2}+&space;3^{2}=&space;5^{2}$  Insert the known values

$A^{2}=&space;5^{2}-3^{2}$  Arrange the values to determine A

$A^{2}&space;=&space;25&space;-&space;9$  Simplify the equation further

$A^{2}=&space;16$

$\sqrt{A^{2}}=\sqrt{16}$

$A=4$

This is the method we use in determining the Hypotenuse of any given triangle.

Where will I use the Pythagoras theorem in real life?

People learn mathematical concepts and often wonder: Where will I use this concept in my day to day life? The Pythagoras theorem can be applied to many instances in life. Whenever the area is involved, we use this theorem. Think of a builder, building a house – trying to work out the shapes and sizes of the rooms. Think of a tiler who needs to tile a certain area. Think of a man working out the amount of wood needed for a single roof truss. Think of a sailor trying to navigate the open sea without a GPS. Think of a land surveyor trying to calculate the steepness of a slope or hill.

There are many instances in which this theorem is used in everyday lives.  To summarise the Pythagoras theorem is used in the following fields.

• Building and construction
• Architecture
• Engineering
• Land surveying

I do hope this guide proves useful in your mathematical journey through highschool. Our development team hope you enjoy the content provided.

Please leave us a comment below should you have any queries or concerns.

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