Question

The only ideas that can be used include: area ABC-RA2(A+B+C-Ipi), the Pythagorean theorem: Cos c-cos a cos b. Vectors-dot product cross product, sin A-sin a/sin c; coS A-COs a sin b/sin c; spherical law of sines, spherical law of cosines for sides and spherical law of cosines for angles

1. Let ABCDE be a regular pentagon on the unit sphere S with each side equal to s and each angle equal to 4pi/5. Find the exact value of cos a. Noticed that as in Euclidean geometry a regular pentagon called a spear can be inscribed in a spherical circle

Answer 1

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