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Two Questions

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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
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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   Jun 27, 2018
#2
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Thank you!  Any tips for the second one?

AnonymousConfusedGuy  Jun 27, 2018
#3
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Sorry, ACG...I don't know the answer to  that one....!!!   CPhill  Jun 27, 2018
#4
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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