# Introduction

In the ancient world, buildings and monuments were often constructed using right-angled triangles.

The important rule about right-angled triangles was formulated by the Greeks, called the Theorem of Pythagoras.

In right-angled triangles, the side opposite to the right angle is called the hypotenuse, as illustrated below:

Remember sometimes that the triangle may be tilted, so it’s not always the same place. However, it is always opposite, relative to the 90 degree angle.

The Theorem of Pythagoras is that the square of the hypotenuse, is equal to the sum of the squares on the other 2 sides, i.e.:

The mathematical notation of the Pythagorean theorem for the above triangle is $c^2=a^2+b^2$

For example:

$c^2=a^2+b^2$
$\therefore 5^2=4^2+3^2$
$\therefore 25=16+9$

Another example:

$x^2=15^2+36^2$
$\therefore x^2=225+1296$
$\therefore x^2=1521$
$\therefore x=39cm$

The opposite to square ($x^2$) is root ($\sqrt(x)$). So the $\sqrt(1521)=39cm$ (use a calculator to find out the root).

Another example:

$53^2=28^2+x^2$
$\therefore x^2=53^2-28^2$
$\therefore x^2=2809-784$
$\therefore x^2=2025$
$\therefore x=45cm$

Another example:

$60^2=x^2+48^2$
$\therefore x^2=60^2-48^2$
$\therefore x^2=3600-2304$
$\therefore x^2=1296$
$\therefore x=36cm$

Word questions in Pythagorean, as in other areas of mathematics, are harder.