Extended Law of Sines

2023-10-03 18:30 作者:第一性原理 0人读过 | 我要投稿

Law of Sines

$%5Cfrac%7Ba%7D%7Bsin%20(A)%7D%3D%5Cfrac%7Bb%7D%7Bsin%20(B)%7D%3D%5Cfrac%7Bc%7D%7Bsin%20(C)%7D$

Proof:

$%5Cmeasuredangle%20C%3D%5Cmeasuredangle%20%5Ctheta%20$

$sin%20(C)%3Dsin%20(%5Ctheta%20)$

$sin%20(%5Ctheta%20)%3D%5Cfrac%7B%5Cfrac%7Bc%7D%7B2%7D%20%7D%7Br%7D%20$

$sin%20(%5Ctheta%20)%3D%5Cfrac%7B%7Bc%7D%7D%7B2r%7D%20$

$%5Cfrac%7Ba%7D%7Bsin%20(A)%7D%3D%5Cfrac%7Bb%7D%7Bsin%20(B)%7D%3D%5Cfrac%7Bc%7D%7Bsin%20(C)%7D%3D2r$

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