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What is the numerical value of the product of the lengths of all diagonals of a regular pentagon of side length 1?

 Sep 5, 2021
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What is the numerical value of the product of the lengths of all diagonals of a regular pentagon of side length 1?

 

Hello Guest!

 

\(\alpha=\frac{180°-72°}{2}=54°\\ sin\ \alpha =\frac{d}{2\cdot 1}\\ d=2\ sin\ \alpha=2\ sin\ 54°\)

\(d=1,618\)

 

The numerical value of the product of the lengths of all diagonals is \(1.618^5=11.09\)

laugh  !

 Sep 5, 2021

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