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!

AnonymousConfusedGuy
Jun 27, 2018

#1**+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

CPhill
Jun 27, 2018

#4**+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