在△ABC 中,a:b:c=3:2:4,则cosC的值为(  ) A.23 B.-23 C.14 D.-14

问题描述:

在△ABC 中,a:b:c=3:2:4,则cosC的值为(  )
A.

2
3

B. -
2
3

C.
1
4

D. -
1
4

由a:b:c=3:2:4,设a=3k,b=2k,c=4k,
则由余弦定理得:cosC=

a2+b2c2
2ab
=
9k2+4k2−16k2
12k2
=-
1
4

故选D