Question

三角形ABC的三内角A,B,C的对边分别为a,b,c.若a=b*根号5/2,A=2B,则cosB等于

Answer 1

s/sinA=b/sinB
a/b=sinA/sinB=√5/2

A=2B
sinA=sin2B
ssinA=2sinBcosB
cosB=(1/2)sinA/sinB=√5/4

Answer 2

a/sinA=b/sinB
a/sin2B=b/sinB
(√5b/2)/(2sinB*cosB)=b/sinB
(√5b/2)/(2cosB)=b
(√5/2)/(2cosB)=1
2cosB=√5/2
cosB=√5/4