Question

在三角形ABC中，若A=60度，a=根号3，b+c=3,b>c,b=?

Answer 1

根据正弦定理，
a/sinA=b/sinB=c/sinC,
a/sinA=(b+c)/(sinB+sinC)
b+c=[√3/（√3/2）]*2sin[(B+C)/2]*cos[(B-C)/2]
=4sin[（180°-A）/2]cos[(B-C)/2]
=4sin(90°-A/2)cos[(180°-60°-C-C)/2]
=4cos(A/2)cos(60°-C)
=4cos30°*cos(60°-C),
=2√3cos(60°-C)=3
cos(60°-C)=√3/2
b>c,则C<60°
C=30°
B=90°
a/sinA=b/sinB
b=√3/(√3/2)=2