The measure of radius c rounded to the nearest hundredth is 12.36
To find the measure of the radius c ,we have to find the angles of regular pentagon first,
Given : A regular pentagon shown, we know that each angle of a regular pentagon is equals to [tex]108\textdegree[/tex] ie. [tex]\angle A=\angle B =\angle C=\angle D=\angle E=108[/tex]°
What is a regular pentagon?
A polygon whose all five sides are equal, here if we sum each angle ie.
[tex]\angle A+ \angle B+\angle C+\angle D+\angle E=540[/tex]°
or, [tex]\angle A= \dfrac{540}{5}=108\textdegree[/tex]
According to the diagram OB will be the angle bisector of [tex]\angle[/tex]B [tex] \dfrac{108}{2}= \angle OBM= 54\textdegree [/tex]
Here, in the triangle OBM,[tex]\angle M[/tex] is a right angle = [tex]90\textdegree[/tex]
Now we use Trigonometric ratio to solve further
[tex] \sin\theta=\dfrac{OM}{OB}[/tex]
[tex]\theta=54\textdegree= \angle B[/tex]
Calculate height h.
[tex]\sin54\textdegree= \dfrac{p}{h}[/tex]
[tex]\sin 54\textdegree= \dfrac{10}{h}\\
\\
\csc54\textdegree= \dfrac{h}{10}\\
\\
h=\csc54\textdegree\cdot10[/tex]
[tex]h=12.36 cm[/tex]
Therefore the measure of radius c is 12.36cm
Learn more about regular pentagon : https://brainly.com/question/10590997
