**The theory**…

Given a right-angle triangle ABC, with sides a, b and c – we can use Pythagoras theorem to find one side of the triangle if we know the two other sides.

**An example**…

Suppose we are given the following:

Triangle ABC is a right angle triangle with side **AB = 4 cm** and side **AC = 8 cm**. Find x (side BC).

**What not to do…** **(THE MISTAKE)**

Unfortunately, many students go into ‘Pythagoras **wrong mode**‘, doing the following.

So side BC equals 8.94 cm – or so they think…. 🙁

Humm….. Well! there are a couple of observations:

- Side BC is one of the shorter sides because in a right angle triangle, the
**hypotenuse is the longest side**. If the hypotenuse is 8 cm then surely side BC must be less than 8. - Looking at the generic pythagoras formula, variable ‘c’ represents the hypotenuse and
**is on the right side of the equation (and on its own)**and yet when replacing the values we have been given, 8 was placed on the left side of the equation next to the value for the shorter side. This is why the steps for working x are not correct.

**What should be done…**

Pythagoras theorem (#1) can be also be written slightly differently (#2) by rearranging the variables. This allows to use the approprite equation based on the values we are given.

And the rule for using the correct equations is…..

- If we are asked to find the
**HYPOTENUSE**then use**#1** - If we are asked to find
**one of the shorter sides**then use**#2**

In our example above, we are asked to find one of the shorter sides, so we use equation #2. Replacing the values we are given into the equation we get:

**In conclusion…**

When using Pythagoras theorem, do bear in mind the following

- If you are asked to
**work out the Hypotenuse**then use the**‘ADD’**equation**(#1)** - If you are asked to
**work out one of the shorter sides**then use the**‘SUBTRACT’**equation**(#2)**

The full lesson on Pythagoras can be found here