[[[[ 1]]]]
This can be obtained from cosine theorem.
- 1/2=cos 120? =cosB=(a? +c? -B? )/(2ac)=(a? +2-6)/(2a√2)
Namely: a? +(√2)a-4=0
(a-√2)(a+2√2)=0
∴a=√2.(a=-2√2 is omitted)
∴a=√2
[[[2]]]
A=60? ,b= 1,S=(√3)/2
Formula by area
(√3)/2 = S =( 1/2)(BC)sinA =(c/2)sin 60? =(c/4)×√3。
∴c=2.
This can be obtained from cosine theorem.
1/2=cos60? =cosA=(b? +c? -a? )/(2bc)=(5-a? )/4
Namely (5-a? )/4= 1/2
Answer? =3
a=√3
[[[3]]]
From the title and sine theorem, we can get
a/sinA=c/sinC=2c/(√3)
∴sinC=(√3)/2
Combining C as an acute angle, we can get C=60?