Question

在三角形ABC中,角A,B,C的对边分别是a,b,c,已知角A等于60度、sinB等于3sinC.求tanC的值.若a等

Answer 1

A=60，则有B+C=120

sinB=3sinC

sin(120-C)=3sinC

sin120cosC-cos120sinC=3sinC

根号3/2cosC=-1/2sinC+3sinC=5/2sinC

故有tanC=根号3/5

sinB=3sinC,即有b=3c

a^2=b^2+c^2-2bccosA

7=9c^2+c^2-2*3c^2*1/2=7c^2

c^2=1, c=1, b=3

S=1/2bcsinA=1/2*3*1*根号3/2=3根号3/4