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Chapter overview

Learning goals

**Learning Goals**

- Learn the 3D pythagoras formula for cuboids

Maths

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So far, you have used Pythagoras' theorem to find lengths of $2$ dimensional shapes. However, Pythagoras' theorem can also applied to find distances in $3$ dimensions.

It is best to show this with a sketch. Here is a cuboid $ABCDEFGH$:

To find the distance $AF$ ($=d$), first use Pythagoras' theorem on triangle $ABH$ to find the distance $AH$, and then use it again on triangle $AFH$ to find the distance $AF$.

*In the cuboid shown above, $a=3cm,b=4cm,d=13cm$*. *Find the value of $c$.*

*Find $AH$ by focusing on the right-angled triangle $ABH$:*

$a^2+b^2=(AH)^2$

$3^2+4^2=(AH)^2$

$(AH)^2=25$

$AH=\sqrt{25}=5cm$

*Then, find $c$ by focusing*