**Pythagoras' Theorem** can be applied on any right-angled triangle, even when it is part of a 3 dimensional shape.

Follow this example to see how it is used to find lengths in 3D shapes.

__Example__

ABCDEFGH is a cuboid (not drawn to scale).

AB = a = 5 cm,

BC = b = 5 cm,

CH = c = 10 cm.

Find the lengths DB and EB in cm to 2 decimal places.

**Answer**

*To find DB*

Look at Triangle DAB, which is right-angled at A.

By Pythagoras' Theorem,

DB^{2} = a^{2} + b^{2} = 5^{2} + 5^{2} = 25 + 25 = 50

**DB** = √50 =** 7.07** cm

*To find EB*

Look at Triangle EDB, which is right-angled at D.

By Pythagoras' Theorem,

EB^{2} = ED^{2} + DB^{2} = 10^{2} + 50 = 100 + 50 = 150

*(Notice how we use the previous fact that DB ^{2} = 50, no need to use the rounded off DB = 7.07.)*

**EB **= √150 = **12.25** cm