Question

在△ABC中，角A，B，C所对的边分别为a，b，c。且满足cosA/2=2根号5/5 ，角b=60° 求sinc

Answer 1

cosA=2(cosA/2)^2-1=3/5,sinA=4/5
B=60°,则cosB=1/2，sinB=√3/2
sinC=sin(π-A-B)=sin(A+B)=sinAcosB+sinBcosA
=4/5*1/2+√3/2*3/5=（4+3√3）/10

Answer 2

cosa=根号5/10 sina=根号95/10 sinb=根号3/2 cosb=1/2
sinc=sin(π-a-b)=-sin(a+b)=-(sinacosb+sinbcosa)
然后代入计算就行了