如图三角形ABC中角A,B,C(C为钝角)所对的边分别为a,b,c,且COS(A+B-C)=1/4.a=2,sin(A+B)/sinA=2求COSC的值求b的长
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![如图三角形ABC中角A,B,C(C为钝角)所对的边分别为a,b,c,且COS(A+B-C)=1/4.a=2,sin(A+B)/sinA=2求COSC的值求b的长](/uploads/image/z/9325564-52-4.jpg?t=%E5%A6%82%E5%9B%BE%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%AD%E8%A7%92A%2CB%2CC%28C%E4%B8%BA%E9%92%9D%E8%A7%92%29%E6%89%80%E5%AF%B9%E7%9A%84%E8%BE%B9%E5%88%86%E5%88%AB%E4%B8%BAa%2Cb%2Cc%2C%E4%B8%94COS%28A%2BB-C%29%3D1%2F4.a%3D2%2Csin%28A%2BB%29%2FsinA%3D2%E6%B1%82COSC%E7%9A%84%E5%80%BC%E6%B1%82b%E7%9A%84%E9%95%BF)
如图三角形ABC中角A,B,C(C为钝角)所对的边分别为a,b,c,且COS(A+B-C)=1/4.a=2,sin(A+B)/sinA=2求COSC的值求b的长
如图
三角形ABC中角A,B,C(C为钝角)所对的边分别为a,b,c,且COS(A+B-C)=1/4.a=2,sin(A+B)/sinA=2求COSC的值求b的长
如图三角形ABC中角A,B,C(C为钝角)所对的边分别为a,b,c,且COS(A+B-C)=1/4.a=2,sin(A+B)/sinA=2求COSC的值求b的长
cos(A+B-C)=1/4
cos(180°-C-C)=1/4
cos2C=-1/4
2cos^2C-1=-1/4
cos^2C=3/8
∵C是钝角
∴cosC=-√6/4
sinC=√(1-cos^2C)
=√(1-3/8)
=√10/4
sin(A+B)/sinA=2
sin(180°-C)/sinA=2
sinC/sinA=2
sinA=(√10/4)/2
=√10/8
cosA=√(1-sin^2A)
=√(1-10/64)
=3√6/8
sinB=sin(180°-(A+C))
=sin(A+C)
=sinAcosC+cosAsinC
=√10/8*(-√6/4)+3√6/8*(√10/4)
=-√15/16+3√15/16
=√15/8
b/sinB=a/sinA
b=a*sinB/sinA
=2*√15/8/(√10/8)
=√6