Hint: use the formula of the area of triangle ABC on the shpere which is easy and given below. The main thing is to find each angles of the triangle. Angles or B and C is 90 degree. What is the angle of A in terms of n?
Area of triangle = R^2(Angle A +Angle B + Angle C).

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Hint: use the formula of the area of triangle ABC on the shpere which is easy and given below. The main thing is to find each angles of the triangle. Angles or B and C is 90 degree. What is the angle of A in terms of n?

Area of triangle = R^2(Angle A +Angle B + Angle C).

Suppose that \\( n \\) is an integer with \\( n>2 \\). Sphere \\( \\mathcal{S} \\) has radius \\( \\frac{n}{\\sqrt{\\pi}} \\). Point \\( A \\) is at the north pole of \\( \\mathcal{S} \\). Point \\( B \\) is on the equator of \\( \\mathcal{S} \\). Point \\( C \\) is on the equator of \\( \\mathcal{S}, \\frac{1}{n} \\) of the way around the equator from \\( B \\). If the area of (spherical) \\( \\triangle A B C \\) is 4046, determine the value of \\( n \\).

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