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avatar+1442 

1:  Find BC in the following triangle, to two decimal places.

 

2:  A soccer ball is constructed using 32 regular polygons with equal side lengths. Twelve of the polygons are pentagons, and the rest are hexagons. A seam is sewn wherever two edges meet. What is the number of seams in the soccer ball?

 

Thanks!

 Jun 27, 2018
 #1
avatar+98107 
+1

Here's 1

 

Angle  ABC  =  180  - 56 -  53  =  180  - 109  =  71°

 

Using the Law of Sines

 

11/  sin ABC  =  BC / sin BAC

 

11 / sin 71  =  BC  / sin 53      multiply both sides by sin 53

 

11 sin 53  / sin 71  = BC ≈   9.29

 

 

cool cool cool

 Jun 27, 2018
 #2
avatar+1442 
+1

Thank you!  Any tips for the second one?

AnonymousConfusedGuy  Jun 27, 2018
 #3
avatar+98107 
0

Sorry, ACG...I don't know the answer to  that one....!!!

 

 

 

cool cool cool

CPhill  Jun 27, 2018
 #4
avatar+1442 
+1

Oh I figured it out!  Since there are 12 pentagons (12 x 5 = 60) there must be 20 hexagons (20 x 6 = 120) so together there are 180 edges but since it is a 3D object we divide that in half for a total of 90 sides.

AnonymousConfusedGuy  Jun 27, 2018

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