LZ,∠A = 60度.x0d
x0d
(tanA-tanB)/(tanA+tanB) = 1 - 2tanB/(tanA+tanB)x0d
(c-b)/c = 1 - b/cx0d
由已知可得,x0d
2tanB/(tanA+tanB) = b/c = sinB/sinC (正弦定理)x0d
x0d
又因为tanA + tanB = (sinAcosB + cosAsinB)/(cosAcosB)x0d
= sin(A+B)/(cosAcosB)x0d
= sinC/(cosAcosB)x0d
x0d
由切化弦得,(2sinB/cosB)/(sinC/(cosAcosB)) = sinB/sinCx0d
化简得到,cosA = 1/2x0d
x0d
所以∠A = 60度.25378希望对你有帮助!