>
数学
>
在△ABC中,已知sin
2
A=sin
2
B+sinBsinC+sin
2
C,则A等于( )
A. 30°
B. 60°
C. 120°
D. 150°
人气:207 ℃ 时间:2020-04-22 13:33:27
解答
根据正弦定理
a
sinA
=
b
sinB
=
c
sinC
=2R,
化简已知的等式得:a
2
=b
2
+bc+c
2
,即b
2
+c
2
-a
2
=-bc,
∴根据余弦定理得:cosA=
b
2
+
c
2
−
a
2
2bc
=-
1
2
,
又A为三角形的内角,
则A=120°.
故选C
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