S=½acsinB
c=2S/(asinB)
=2(3+√3)/[(2√3)×sin45°)
=2(3+√3)/[(2√3)(√2/2)]
=2(3+√3)/√6
=√6+√2
由余弦定理得
b²=a²+c²-2accosB
=(2√3)²+(√6+√2)²-2(2√3)(√6+√2)(√2/2)
=8
b=2√2
由正弦定理得
c/sinC=b/sinB
sinC=csinB/b=(√6+√2)sin45°/(2√2)=(√6+√2)/4
a/sinA=b/sinB
sinA=asinB/b=(2√3)sin45°/(2√2)=√3/2 A=60°或A=120°
A=120°時(shí),C=180°-45°-120°=15° sinC