spherical trigonometry?

2011-07-24 3:17 pm

A triangle is now drawn on a sphere. If I know the length of the 3 sides of the triangle and the radius of the circle, how to calculate the area of the triangle??

回答 (2)

[匿名]

2011-07-24 3:34 pm

✔ 最佳答案

Given sides a, b, and c, and angles A, B, and C, we can find one angle from the law of cosines

cosc = cosa cosb + sina sinb cosC, then use the law of sines to find the other two angles

If E = A + B + C – 180, then

A = R²E

(Remember that the sides of a spherical triangle are segments of great circles, so there measure is given by an arc, not a length. Hence the sines and cosines of the sides. Note also that the sum of the angles of a spherical triangle is greater that 180°, so E > 0

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Ed I

2011-07-24 10:20 pm

I would think you could use Heron's Formula, even it is a spherical triangle.

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