升幂公式:1+cosB=2(cosB/2)^2(这是公式,不记得就找书)
变形cosB=2(cosB/2)^2-1
=8/5-1
=3/5,
sinB=4/5,
根据正弦定理,
c/sinC=a/sinA
c=(a*sinC)/sinA=(2sinπ/4)/sin[π-(B+C)]
=√2/(sinBcosC+cosBsinC)
=√2/[(4/5)*√2/2+(3/5)*√2/2]
=10/7
S=1/2*ca*sinB =1/2*10/7*2*4/5=8/7
升幂公式:1+cosB=2(cosB/2)^2(这是公式,不记得就找书)
变形cosB=2(cosB/2)^2-1
=8/5-1
=3/5,
sinB=4/5,
根据正弦定理,
c/sinC=a/sinA
c=(a*sinC)/sinA=(2sinπ/4)/sin[π-(B+C)]
=√2/(sinBcosC+cosBsinC)
=√2/[(4/5)*√2/2+(3/5)*√2/2]
=10/7
S=1/2*ca*sinB =1/2*10/7*2*4/5=8/7