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.
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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.
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Let's use Pythagoras to solve for the missing length on these two triangles
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Notice that the hypotenuse of the lower triangle is one of the legs of the upper triangle, so let's solve for that hypotenuse
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Root 13 is not an integer, so let's leave it as a radical
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Now we can use Pythagoras to solve for the upper triangle
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Root 13, squared, is just 13, so we have the root of 49 as our missing length
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So that length is 7