高一数学：S三角形ABC=0.5,ac=2,sinA=cosC,求角A

S=1/2acsinB
1/2acsinB=0.5
1/2×2×sinB=1/2
sinB=1/2
sinA=cosC
sinA=cos(180-A-B)
sinA=-cos(A+B)
sinA=sinAsinB-cosAcosB
sinA-1/2sinA=-cosAcosB
1/2sinA+cosAcosB=0
cosAcosB+sinAsinB=0
cos(A-B)=0
A-B=π/2
因为sinB=1/2
所以B=π/6
A=π/2+π/6=2π/3