Aregular pentagon is shown.

what is the measure of the radius, c, rounded to the nearest hundredth? use an appropriate trigonometric ratio to solve.

5.88 cm
8.09 cm
12.36 cm
17.01 cm

we know that

The formula to calculate the sum of the internal angles of a polygon is equal to

where

n is the number of sides

In this problem we have a  regular pentagon

so

substitute

Find the internal angle of a regular pentagon

In the right triangle of the figure

solve for c

therefore

the answer is the option

The measure of radius c is 12.36 cm

C is correct.

Step-by-step explanation:

Given: A regular pentagon is shown in diagram.

As we know the sum of angle of pentagon is 540°

It is a regular pentagon. Therefore, each angle is equal.

OB would be angle bisector of angle B

Thus,

In triangle OBC, ∠C=90°

Hence, The measure of radius c is 12.36 cm