Suppose T is an equilateral triangle on the sphere of radius R = 1. Let a denote

Question

Suppose T is an equilateral triangle on the sphere of radius R = 1. Let a denote the angle at any of the three vertices

Explanation / Answer

soll.. Suppose T is an equilateral triangle on the sphere of radius R=1. Let a denote the angle at any of the three vertices’s of the triangle. (Recall that 3a>n.) Use the result of the last problem on the previous homework and the inclusion - exclusion principle (together with an orange and a knife) to compute the area of T . I assumed that all angle on the equilateral triangle where 90 degrees or p2; therefore making the volume equal to 1/8 that of the whole sphere So I did A=a2R2 where A is the area of T A=p22R2 A=p*R2 That would be the area of 1/4 of the sphere overall, but because I am taking the area of an equilateral triangle, I took half of that to get A=p2R2 A=p2*1 A=p2 Would that be correct? I just kind of picked 90 degrees or p2 for a, but I assume it could be anything between 60 and up to 90...

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