A equiangular triangle is now drawn on a sphere. If the side of the triangle is (pi)/3 and the radius of the sphere is 1, what's the area of the triangle.[By using spherical law of cosines and E = A + B + C – 180]
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spherical trigonometry?
2011-07-24 4:44 pm
回答 (1)
2011-07-27 1:34 pm
✔ 最佳答案
Spherical law of cosines states cos(c) = cos(a)cos(b) + sin(a)sin(b)cos(C) (lower case the sides ; upper case the angles!)
using to get cos C :
cos pi/3 = cos pi/3 cos pi/3 + sin pi/3 sin pi/3 cos C
0.5= 0.25 + sqrt(3)/2 *sqrt(3)/2 *cos C
1/4 = 3/4 * cos C
1/3 = cos C
C= 1.231 rad
equilateral triangle so all angles the same.
Area of triangle is R^2 * E
E = A+B+C -pi (must work in radians!)
E= 1.231 *3 - pi = 0.5513
Area is 0.5513
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