Question

在三角形ABC中,B=45度,a/c=√2,则C=_____度?

Answer 1

B=45°

则A+C=180-B=135°

A=135°-C

a/sinA=c/sinC

a/c=sinA/sinC

根号2 = sinA/sinC = sin(135°-C)/sinC

sin(135°-C) = 根号2 sinC

sin135°cosC - cos135°sinC = 根号2 sinC

根号2/2 cosC + 根号2/2 sinC = 根号2 sinC

cosC + sinC = 2 sinC

sinC=cosC

tanC=1

C=45°