Question

已知△abc所对的边分别为a.b.c △abc的面积为s 且ba与bc的数量积为s

已知△ABC的内角A、B、C所对边的长分别为a、b、c,若ac=5,且向量BA×向量BC=√5.﹙1﹚求△ABC的面积大小及tanB的值；

Answer 1

S= △ABC的面积
= (1/2) |AB||BC|sinB
= (1/2) (AB.BC) tanB
= (-1/2) √5 tanB (1)
ac = 5
|BC||AB| =5
S = (1/2) |AB||BC|sinB = (5/2) sinB (2)
(1) =(2)
=>(-1/2) √5 tanB = (5/2) sinB
cosB = -√5/5
tanB = -2
△ABC的面积=S = (-1/2) √5 tanB = (-1/2) √5 (-2) = √5