+0  
 
0
78
1
avatar

Find the radius of a circle circumscribed in a regular pentagon whose perimeter is 28 inches.

Guest Apr 3, 2017
Sort: 

1+0 Answers

 #1
avatar+76918 
+2

 

 

I think you must mean "inscribed" if the circle is inside the regular pentagon...

 

Look at this picture to get a good idea of the situation :

 

 

AE  =  28/5 inches  =   5.6 inches....so AM is 1/2 of this  =  2.8 inches

Angle AFE  =  360/5 = 72°.....so.....angle AFM is 1/2 of this  = 36°

And angle BAE = 108°.....so......angle FAM is 1/2 of this  = 54°

And FM is the radius of the circle which can be found using The Law of Sines

 

AM / sin AFM  = FM / sin FAM

2.8 / sin 36° = FM /  sin 54°

Rearrange  as

FM  = sin 54° * 2.8 / sin 36°  ≈ 3.854 inches

 

 

cool cool cool

CPhill  Apr 3, 2017
edited by CPhill  Apr 3, 2017
edited by CPhill  Apr 3, 2017

31 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details