It's all Greek to me

The Greek mathematician Pythagoras happened to discover a theorem which has been taught in mathematics classes ever since. Here is a picture of Pythagoras in case you were wondering what he looked like:
Pythagoras apparently used to scratch out diagrams in the sand on a beach to explain his latest mathematical discoveries. However as Robert Ainsley puts it in his witty book Bluff Your Way in Maths: "Pythagoras was the first person to breed a hypotenuse in captivity.....He met his end when he told a Roman Soldier to stop walking over his hypotenuses and the soldier, who decided he couldn't stand a smart-arse, killed him".


Pythagoras' theorem is as follows:

In a right angled triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides.

Key:
Right-angled triangle - Means a triangle which has an angle of 90 degrees between two of its sides.

Hypotenuse - Is a fancy name for the longest side in a right-angled triangle.

Here's diagram to show you where the hypotenuse is:
The hypotenuse can be clearly seen as the longest side of the triangle. The other sides of the triangle are labelled as opposite (opposite the angle a) and adjacent (next to the angle a) - you'll use these more in trigonometry.


An easy way to visualise Pythagoras' Theorem is by using a diagram like this:

If you draw a right angled triangle (like the red one here), then extend each of the sides of the triangle so that they make squares. Cut out the squares, with a bit of cutting and matching you'll find that bits of both of the blue squares put together will fit exactly over the yellow square.

In other words, the square created from the hypotenuse = the square from the opposite side + the square from the adjacent side.

This can be shown in algebra as:

h2 = o2 + a2


Whenever you see right-angle triangle problems and you are given the lengths of two of the sides, then you can always calculate the length of the unknown side by using Pythagoras' Theorem.

For example:

A roof has a height at the centre of 3m and the length from the centre of the roof to the edge is 4m as shown in the diagram.
Calculate the length of the sloping part of the roof.

This is a classic Pythagoras problem. To solve it first write out Pythagoras' Theorem using the values you know and call the hypotenuse x (unknown).

x2 = 32 + 42

The rest is easy (if you know a bit of algebra...)

x2 = 9 + 16

x2 = 25

x = square root of 25 which is 5.

Hence the answer is 5m (REMEMBER THE UNITS)