Question

△ABC中,A=,BC=3,则△ABC的周长为(    )

A.4sin(B+)+3                       B.4sin(B+)+3

C.6sin(B+)+3                             D.6sin(B+)+3

 

Answer 1

解析：设AB=c,AC=b,

∵==,

∴==2.

∴a+b+c=2(sinB+sinC+)

=2×2sin·cos+3.

∵B+C=180°-A=120°,

∴C=120°-B.

∴sin·cos

=sin60°·cos

=sin60°·cos(B-60°)

=cos［90°-(B+30°)］

=sin(B+30°)

=sin(B+).

∴a+b+c=6sin(B+)+3.

答案：D