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对于非直角三角形，可以使用两种规则
用于求边长 a sin ( A ) = b sin ( B ) = c sin ( C ) {\displaystyle {\frac {a}{\sin(A)}}={\frac {b}{\sin(B)}}={\frac {c}{\sin(C)}}} 重新排列以求角度 sin ( A ) a = sin ( B ) b = sin ( C ) c {\displaystyle {\frac {\sin(A)}{a}}={\frac {\sin(B)}{b}}={\frac {\sin(C)}{c}}}
用于求边长 a 2 = b 2 + c 2 − 2 b c cos ( A ) {\displaystyle a^{2}=b^{2}+c^{2}-2bc\cos(A)} b 2 = a 2 + c 2 − 2 a c cos ( B ) {\displaystyle b^{2}=a^{2}+c^{2}-2ac\cos(B)} c 2 = a 2 + b 2 − 2 a b cos ( C ) {\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos(C)} 重新排列以求角度 cos ( A ) = b 2 + c 2 − a 2 2 b c {\displaystyle \cos(A)={\frac {b^{2}+c^{2}-a^{2}}{2bc}}} cos ( B ) = a 2 + c 2 − b 2 2 a c {\displaystyle \cos(B)={\frac {a^{2}+c^{2}-b^{2}}{2ac}}} cos ( C ) = a 2 + b 2 − c 2 2 a b {\displaystyle \cos(C)={\frac {a^{2}+b^{2}-c^{2}}{2ab}}}
一个三角形的例子，边长分别为a、b和c，角分别为A、B和C。
The Wikibooks community is developing a policy on the use of generative AI. Please review the draft policy and provide feedback on its talk page.
