数学三角形邱求值

cosB=-5/13
0<B<180
所以sinB>0
且sin²B+cos²B=1
所以sinB=12/13
同理
sinC=3/5
sinA=sin[180-(B+C)]
=sin(B+C)
=sinBcosC+cosBsinC
=33/65

S=1/2bcsinA=33/2
bc=65
令k=b/sinB=c/sinC=a/sinA
则k²=bc/sinBsinC=(a/sinA)²
所以65/(12/13*3/5)=[a/(33/65)²]
a=11/2
即BC=11/2

B=pi-arccos(5/13)
C=arccos(4/5)
A=pi-[pi-arccos(5/13)]-arccos(4/5)=arccos(5/13)-arccos(4/5)
①
sinA=sin[arccos(5/13)-arccos(4/5)]
=sin[arccos(5/13)]cos[arccos(4/5)]-cos[arccos(5/13)]sin[arccos(4/5)]
=12/13 *4/5-5/13 *3/5
=48/65-3/13
=33/65

②
BC上的高AD交CB延长线于D，AD/BD=tan角ABD=12/5
BD=5AD/12
AD/CD=tanC=3/4
AD=3CD/4=3（BC+BD）/4=3（BC+5AD/12）/4=3BC/4+5AD/16
11AD/16=3BC/4
AD=12BC/11
三角形面积等于 二分之三十三
1/2 *AD*BC=33/2
12BC/11 *BC=33
BC^2=121/4
BC=11/2

1、cosB=-5/13，sinB=√[1-(cosB)^2]=12/13,
sinC=√[1-(cosC)^2]=3/5,