Question

如图求过程

Answer 1

a+c=2b
正弦定理
sina/a=sinb/b=sinc/c
sina+sinc=2sinb
A=120+C
A+B+C=180
C=30-B/2
A=150-B/2
sinA+sinC=sin(30-B/2)+sin(150-B/2)=cosB/2=2sinB4sinB/2=1,sinB/2=1/4,cosB/2=√15/4sinC=sin30cosB/2-sinB/2cos30=√15/8-√3/8sinA=sin150cosB/2-sinB/2cos150=√15/8+√3/8

Answer 2

2b=a+c
2sinB=sinA+sinC
2sin(A+C)=sinA+sinC
4sin(A+C)/2*cos(A+C)/2=2sin(A+C)/2*cos(A-C)/2
2cos(A+C)/2=cos(A-C)/2
2cos(A+C)/2=1/2
2sinB/2=1/2
sinB/2=1/4
cosB/2=√15/4
A-C=120
A+B+C=180
C=30-B/2
A=150-B/2
sinA=sin(150-B/2)=1/2cosB/2+√3/2sinB/2
=1/2*√15/4+√3/2*1/4
=(√3+√15)/8
sinC=sin(30-B/2)=1/2cosB/2-√3/2sinB/2
=1/2*√15/4-√3/2*1/4
=(√15-√3)/8