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

Answer:12.36

Explanation:

just did it

Answer 2

The angle at the center opposite side b must be


`\theta = \frac 1 2 \cdot (360^\circ)/(5) = 36^\circ`


`\cos \theta = (10)/(c)`


`c = (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 =(10)/(\frac 1 4 (1+\sqrt 5)) = 10(\sqrt 5 - 1)`