三角形ABC中,已知COS A =3/5,SIN B=5/13,求SIN C的值

题目

三角形ABC中,已知COS A =3/5,SIN B=5/13,求SIN C的值

答案

假设AB边高h
sinA=4/5=h/b
sinb=5/13=h/a
a=52b/25
c=bcosA+acosB=3b/5+12a/13=63b/25
sinC=c*sinB/b
=(63b/25)*(5/13)/b
=63/65