Question

在△ABC中，若a+c=1，C=45°，B=30°，则b=

Answer 1

过点A做AD垂直BC于点D，设CD=x

∵∠C=45，∠B=30，则AD=CD=x，AB=2，BD=√3x

∵a+c=1

∴3x+√3x=1

x=(3-√3)/6

b=√2×(3-√3)/6

  =(3√2-√6)/6

Answer 2

<A=180º-<B-<C=105º
由正弦定理得
a=2Rsin105²=2Rsin(45º+30º)=2R(sin45ºcos30º+sin30ºcos45º)
=2R(√2/2×√3/2+√2/2×1/2)=2R(√6/4+√2/4)=R(√6+√2)/2
c=2Rsin45º=2R(√2/2)=√2R
∵a+c=1
∴R(√6+√2)/2+√2R=1
R(3√2+√6)=2
R=2/(3√2+√6)=(3√2-√6)/6
∴b=2Rsin30º=R=(3√2-√6)/6

Answer 3

△ABC中 C=45°，B=30°那么A=105°
a/sin105°=c/sin45°
(√2/2)a=[(√6+√2)/4]c
a=[(√3+1)/2]c
a+c=1 [(√3+1)/2]c+c=1
c=2/(√3+3)=(3-√3）/3
b/sin30°=c/sin45°
b=sin30°c÷sin45°
=1/2×(3-√3)/3÷√2/2
=1/2×(3-√3)/3×√2
=(3√2-√6)/6