Question

在三角形ABC中,a,b,c分别是角A,B,C所队的边,A=派/3,a=√3,b+c=3,则三角形ABC的面积S=

Answer 1

A=π/3

a=√3

b+c=3

根据余弦定理a^2=b^2+c^2-2bccosA

3 = b^2+c^2-2bc*1/2 = b^2+c^2-bc = (b+c)^2-3bc = 3^2-3bc

bc = 2

S=1/2bcsinA = 1/2*2*sinπ/3 = √3/2