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

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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:

$$6^2 + 8^2 = d^2$$​​

$$36+64=d^2$$​​

$$d^2 = 100$$​​

​$$\underline{d = \sqrt{100} = 10}$$​