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Pythagoras Theorem – Are you making this mistake ?

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:

  1. 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.
  2. 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