三角形ABC中,角A:角B:角C
A:B:C=1:2:4;& A+B+C=pi--->A=pi/7;B=2A=2pi/7;C=4A=4pi/7。
a/sinA/b/sinB/c/sinC=2R
--->1/BC=2RsinA;1/CA=2RsinB;1/AB=2RsinC
--->1/AB+1/CA=2R/sinC+2R/sinB
=2R(sinB+sinC)/(sinBsinC)=2R(sin4A+sin2A)/(sin2Asin4A)
=2R(2sin3AsinA)/(2sin4AsinAcosA)
=2R(sin3A)/(sin4AsinA)[3A=pi-4A]
=2Rsin4A/(sin4AsinA)
=2R/...全部
A:B:C=1:2:4;& A+B+C=pi--->A=pi/7;B=2A=2pi/7;C=4A=4pi/7。
a/sinA/b/sinB/c/sinC=2R
--->1/BC=2RsinA;1/CA=2RsinB;1/AB=2RsinC
--->1/AB+1/CA=2R/sinC+2R/sinB
=2R(sinB+sinC)/(sinBsinC)=2R(sin4A+sin2A)/(sin2Asin4A)
=2R(2sin3AsinA)/(2sin4AsinAcosA)
=2R(sin3A)/(sin4AsinA)[3A=pi-4A]
=2Rsin4A/(sin4AsinA)
=2R/sinA
=1/BC
。收起