Inscribed and described circle

Find the radii of a circle inscribed and circumscribed by a regular pentagon whose side measures 3 cm.

Correct result:

r =  2.0646 cm
R =  2.552 cm

Solution:

a=3 cm n=5 α=π/n=3.1416/5≐0.6283 rad  r=a2⋅ tan⁡(α)=32⋅ tan⁡(0.6283)=2.0646 cm
R=a2⋅ sin⁡(α)=32⋅ sin⁡(0.6283)=2.552 cm

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