Use of Pythagorean Theorem

One of the most important formulas in math is Pythagorean theorem which is named after Greek philosopher Pythagoras (even though its formulation is historically unknown). The importance of Pythagorean theorem lies in the fact that it can be used to find the length of the side of a right triangle, provided the length of the two other sides is known. It is given by:

Where c is the longest side  of the triangle (also known as hypotenuse), and a and b are the two other sides in no particular order.  The right triangle with its corresponding sides is shown in the figure below.

Now we can take a look at a simple example of how we can use Pythagorean theorem to find the length of a side.

Example:

Find the length of the hypotenuse of a right triangle in which the two other side have lengths of 3 and 4 units, accordingly.

Solution:

We can sketch the right triangle described in the problem statement. The triangle below is not drawn to scale.

By using Pythagorean theorem, we can calculate the length of the hypotenuse as shown below.

The length of the hypotenuse of this right triangle is 5 units.

Closing Remarks:

Right angles and triangles are very common. They appear all around us, thus the applications of Pythagorean theorem are endless. This makes it a very powerful formula which must be dominated by any math student. We will see it over and over again!