(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The area of an equilateral triable is Pi/2.

1) Find the magnitude of its angles

2) Find the length of its sides

3) Find the area of its strict dual

2. Relevant equations

Area + Pi = sum of 3 angles

cosa=cosbcosc + sinbsinccosu

cosu=cosvcosw + sinvsinwcosa for sides length a,b,c and opposite angles of magnitude u,v,w

3. The attempt at a solution

1) I used the formula involving area, so Pi/2 + Pi = 3(magnitude of angle) so the answer is Pi/2. Assuming equilateral means the same in spherical geometry?

2) I used the cos formula with a=b=c, and the angle is Pi/2, getting to cosa= 0, a=Pi/2, or cosa=1, a=0, so a=Pi/2.

3) Considering the dual triangle to the triangle with sides a, b, c. This dual triangle has sides

Pi − u, Pi − v, Pi − w. So we would get that the triangle has sides length Pi/2 again. So area Pi/2 again? I'm not very convinced about this.

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# Homework Help: Spherical geometry

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