Question

abc外接圆半径为根号三,内角ABC对边分别为abc,若A=60,b=2则c的值为?A根号6+1 B根号6-1 C根号6

Answer 1

由正弦定理a/sinA=b/sinB=c/sinC=2r得,

a/sin60°=2/sinB=2√3

∴a=2√3*(√3/2)=3

sinB=2/(2√3)=√3/3

∴sinC=sin(A+B)=sinAcosB+cosAsinB=(√3/2)(√6/3)+(1/2)(√3/3)=(3√2+√3)/6

∴c=2√3*[(3√2+√3)/6]=√6+1

∴选A