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Pythagoras in 3D with a double triangle

This math skill demonstrates the use of the Pythagorean theorem in a three-dimensional context using two connected triangles. The skill illustrates how to solve for unknown side lengths sequentially by utilizing previously calculated hypotenuses as legs in additional triangles.

Learn Pythagoras in 3D with a double triangle

Teaching Transcript

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Let's use Pythagoras to solve for the missing length on these two triangles

Notice that the hypotenuse of the lower triangle is one of the legs of the upper triangle, so let's solve for that hypotenuse

Root 13 is not an integer, so let's leave it as a radical

Now we can use Pythagoras to solve for the upper triangle

Root 13, squared, is just 13, so we have the root of 49 as our missing length

So that length is 7

Skill Practice

Pythagoras in 3D with a double triangle

Test your understanding of Pythagoras in 3D with a double triangle by practicing it! Work through the below exercises to use it in practice.