# geometry

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what is the length of any diagonal of a regular pentagon with a side of 20mm ?

• Geometry quick i have test tomorrow -

what is the length of any diagonal of a regular pentagon with a side of 20mm

• geometry -

first find the size of each interior angle
angle = 180(5-2)/5 = 108°

let the length of the diagonal be x
by cosine law
x^2 = 20^2 + 20^2 -2(20)(20)cos 108°

I am sure you can finish it from there.

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