1.
cos(π/4-A)=cos(π/4)cosA+sin(π/4)sinA=(√2/2)(sinA+cosA)=√2/10
sinA+cosA=1/5
cosA=1/5 -sinA
sin²A+cos²A=1
sin²A+(1/5 -sinA)²=1
整理,得
25sin²A -5sinA-12=0
(5sinA+3)(5sinA-4)=0
sinA=-3/5(A为三角形内角,sinA>0,舍去)或sinA=4/5
sinA=4/5
2.
S=(1/2)bcsinA
c=2S/(bsinA)
=2×12/(6×4/5)
=5
cosA=1/5-sinA=1/5 -4/5=-3/5
由余弦定理得
a²=b²+c²-2bccosA
=6²+5²-2×6×5×(-3/5)
=36+25+36
=97
a=√97