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A regular pentagon is shown. What is the measure of the radius, c, rounded to the nearest hundredth? Use an appropriate trigonometric ratio to solve.

A regular pentagon is shown What is the measure of the radius c rounded to the nearest hundredth Use an appropriate trigonometric ratio to solve class=

Respuesta :

DeanR
The angle at the center opposite side b must be 

[tex]\theta = \dfrac 1 2 \cdot \dfrac{360^\circ}{5} = 36^\circ[/tex]

[tex]\cos \theta = \dfrac{10}{c}[/tex]

[tex]c = \dfrac{10}{\cos 36^\circ} = 12.36[/tex]

Did you know the cosine of [tex]36^\circ[/tex] was half the Golden Ratio? We can actually get an exact answer for this one.

[tex]c =\dfrac{10}{\frac 1 4 (1+\sqrt 5)} = 10(\sqrt 5 - 1)[/tex]



rocasparkz

Answer:12.36

Step-by-step explanation:

just did it