Question

已知在三角形abc中,a=2倍根3,b=45度,S=3+根3,求b,c,A,C

Answer 1

S=½acsinB

c=2S/(asinB)

=2(3+√3)/[(2√3)×sin45°)

=2(3+√3)/[(2√3)(√2/2)]

=2(3+√3)/√6

=√6+√2

由余弦定理得

b²=a²+c²-2accosB

=(2√3)²+(√6+√2)²-2(2√3)(√6+√2)(√2/2)

=8

b=2√2

由正弦定理得

c/sinC=b/sinB

sinC=csinB/b=(√6+√2)sin45°/(2√2)=(√6+√2)/4

a/sinA=b/sinB

sinA=asinB/b=(2√3)sin45°/(2√2)=√3/2 A=60°或A=120°

A=120°时,C=180°-45°-120°=15° sinC