Question

在△abc中,a、b、c分别是内角A、B、C所对的边,c=π/3,a=根号3，若向量m=（1，sinA）,n=(2，sinB),且m∥n.

1.求b，c的值
2.求角A的大小及△ABC的面积

Answer 1

(1)
C=π/3, a=√3
m//n
=>1/sinA=2/sinB
sinB=2sinA
By sine-rule
a/sinA = b/sinB
a/sinA = b/(2sinA)
√3 = b/2
b = 2√3
By cosine-rule
c^2 = a^2 +b^2 -2abcosC
= 3 + 12 - 6
=9
c =3
(2)
a/sinA = c/sinC
√3/sinA = 3/(√3/2)
sinA = 1/2
A = π/6
△ABC的面积
= (1/2)bcsinA
=(1/2)(2√3)(3)(1/2)
=3√3/2