Inscribed and described circle

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

Correct answer:

r =  2.0646 cm
R =  2.552 cm

Step-by-step explanation:

$$\begin{gathered} a=3\text{ cm } \\ n=5 \\ \alpha =\pi \mathrm{/}n=3.1416\mathrm{/}5\doteq 0.6283\text{ rad } \\ r={\displaystyle \frac{a}{2\cdot \tan (\alpha )}}={\displaystyle \frac{3}{2\cdot \tan (0.6283)}}=2.0646\text{ cm} \end{gathered}$$

$R={\displaystyle \frac{a}{2\cdot \sin (\alpha )}}={\displaystyle \frac{3}{2\cdot \sin (0.6283)}}=2.552\text{ cm}$

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