amaths

By Sine Formula, we have
sin B/b = sin C/c
sin B/sin C = b/c

Given that b sin B = c sin C. We have sin B/sin C = c/b.
So b/c = c/b.
b^2 = c^2
Because b and c are positive, we have
b = c.

Therefore, triangle ABC is an isoscles triangle.

bsinB=csinC------1

根據sine law,

b/sinB=c/sinC
b=csinB/sinC------2

把2代入1中,
c(sinB)^2=c(sinC)^2
所以角B=角C~
triangle ABC is a isosceles triangle