Question

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.

Answer 1

The angle at the center opposite side b must be 

$\theta = \dfrac 1 2 \cdot \dfrac{360^\circ}{5} = 36^\circ$

$\cos \theta = \dfrac{10}{c}$

$c = \dfrac{10}{\cos 36^\circ} = 12.36$

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

$c =\dfrac{10}{\frac 1 4 (1+\sqrt 5)} = 10(\sqrt 5 - 1)$

Answer 2

Answer:12.36

Step-by-step explanation:

just did it