Question

设三角形ABC的内角ABC的对边分别为abc,已知A-C=90°，a+c=根号下2倍的b.求C哪位办帮帮忙！！谢谢

Answer 1

a+c=根号2b。
sinA+sinC=根号2sinB,
sin(90+C)+sinC=根号2sin(A+C),
cosC+sinC=根号2sin(90+2C),
cosC+sinC=根号2cos2C,
cosC+sinC=根号2(cos^2C-sin^2C)
cosC+sinC=根号2(cosC+sinC)( cosC-sinC)
由已知C是锐角，所以根号2( cosC-sinC)=1，
2cos (C+45) =1，C+45=60,C=15度.

Answer 2

A+B+C=180
B=180-A-C=90-2C
sinA+sinC=根号2sinB
sin(90+c)+sinC=根号2sin(90-2C)
cosC
cosC+sinC=根号2cos2C
1+sin2C=2cos^22C =>sin2C=cos4C
sin2C=1-2sin^22C =>sin2C=1/2 2C=π/6或5π/6（舍) 因为A-C=90
C=π/12 望采纳 谢谢

Answer 3

我是打酱油的。。。。。