a=3 ，b=4， SinA=3/5，则SinC=？

a=3 ，b=4， SinA=3/5，则SinC=？

sinA =3/5
=>cosA =4/5 or -4/5

b/sinB =a/sinA
sinB = bsinA/a
=4(3/5)/3
= 4/5

=>cosB = 3/5 or -3/5

case 1: cosA =4/5 , cosB =3/5
sinC = sin(A+B)
= sinAcosB + cosAsinB
=(3/5)(3/5) + (4/5)(4/5)
=1

case 2: cosA =-4/5 , cosB =3/5
sinC = sin(A+B)
= sinAcosB + cosAsinB
=(3/5)(3/5) + (-4/5)(4/5)
=-7/25
rejected sinC >0

case 3: cosA =4/5 , cosB =-3/5
sinC = sin(A+B)
= sinAcosB + cosAsinB
=(3/5)(-3/5) + (-4/5)(4/5)
=7/25

case 4: cosA =-4/5 , cosB =-3/5
sinC = sin(A+B)
= sinAcosB + cosAsinB
=(3/5)(-3/5) + (-4/5)(4/5)
=-1 (rejected)
ie
sinC =1 or 7/25

根据正弦定力，可得sinB=4/5
因为b＞a，
所以，cosB=3/5或者-3/5
,cosA=4/5
sinC=sin(π-A-B)=sin(A+B)=sinA cosB+cosA sinB
当cosB=3/5 时，sinC=1，此时C=90
当cosB=-3/5时，sinC=7/25

SinA=3/5
cosA=4/5或cosA=－4/5
a^2=c^2+b^2-2bccosA
c^2+16-32/5*c=9
5c^2-32c+35=0
c=5或c=7/5
SinC=c/a*SinA=5/3*3/5=1 或SinC=c/a*SinA=7/5/3*3/5＝7/25
1或7/25