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Pythagoras' theorem

Tutor: Bilal

# Pythagoras' theorem

## In a nutshell

Pythagoras' theorem is very useful when trying to find the value for the third side of a right-angled triangle. Additionally, at this level, you may have to apply the formula to finding the distance between 2 points on a graph.

## Recap

Pythagoras' theorem says that:

$a^2+b^2=c^2$

Where $a$​ and $b$​ are the two shorter sides of a right-angled triangle and $c$​ is the hypotenuse.

Note: Pythagoras' theorem only works for a right-angled triangle. If there is no right-angle, then you cannot use Pythagoras' theorem.

### Hypotenuse

The hypotenuse of a triangle is the longest side. For a right-angled triangle, the hypotenuse is always the side opposite the right-angle.

## Distance between two points on a graph

You may be asked to find the distance between 2 given coordinates. Approaching these types of problems always requires the same method.

#### PROCEDURE

 1 Do a quick sketch of the graph with the given coordinates and draw a right-angled triangle with the two points. 2 Find the lengths of the two shorter sides of the triangle. 3 Use Pythagoras' theorem to find the length of the hypotenuse of the triangle - this is the distance.

##### Example

Find the distance between the points $A (-1,3)$​ and $B(5,-5)$.

First, make a quick sketch:

The length of the horizontal side is:

$5 - (-1) = 6$

The length of the vertical side is:

$3 - (-5) = 8$

The distance (labelled $d$) will then satisfy Pythagoras' theorem:

$6^2 + 8^2 = d^2$​​

$36+64=d^2$​​

$d^2 = 100$​​

$\underline{d = \sqrt{100} = 10}$

## FAQs - Frequently Asked Questions

### When can I use Pythagoras' Theorem?

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