Use Pythagoras theorem in 3-D problems
Working in 3D can be made easy - by working with it in 2D.
Given a 3D shape, you can imagine cutting the shape up to give you a slice, which is flat along where you cut it (and 2D!)
You need to be able to recognise 2D shapes (flat surfaces) within these 3D shapes.
For example: [picture missing]
We can still use pythagoras’ theorem to find missing sides and angles, but sometimes there are two steps to the problem.
For example, consider this cuboid.
We want to find length AD.
Length AD is also the hypotenuse in the right-angled triangle, with AC and CD as the other 2 sides.
But first we need to calculate AC because it is not given to us.
AC is also the hypotenuse in another triangle ABD.
AC2 = AB2 + BD2 = 42 + 32 = 52
Now, we have AC and CD, we can calculate AD
AD2 = AC2 + CD2 = 52 + 22 = 29
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