Question

在△ABC中,角A,B,C所对的边分别是a,b,c,且满足cos(A/2)=2√5/5,向量AB乘以向量AC等于3.①求

Answer 1

由题可得出

① cosA=2[cos(A/2)]^2-1=3/5 ,sinA=4/5.

向量AB*AC = |AB|*|AC|*3/5 = 3,

∴S△ABC = (1/2)|AB|*|AC|sinA = 2.

② 由①得,b=5.

∴a^2 = 25+1-10*3/5 = 20,

∴a = 2√5