问题 解答题
在△ABC中,角A,B,C所对的边分别为a,b,c满足bcosC+
1
2
c=a.
(1)求角B;
(2)若a,b,c成等比数列,判断△ABC的形状.
答案

(1)因为bcosC+

1
2
c=a.

由正弦定理可知:sinBcosC+

1
2
sinC=sinA,

sinBcosC+

1
2
sinC=sinBcosC+cosBsinC,

cosB=

1
2
,B为三角形内角,

所以B=

π
3

(2)因为a,b,c成等比数列,所以b2=ac,

由余弦定理b2=a2+c2-ac,

可得a2+c2-2ac=0,a=b=c,

所以三角形为等边三角形.

阅读理解

Everybody is afraid of something.That’s what more than 1,700 kids told us when we asked them about fears and scary stuff.We gave kids a list of 14 scary things and asked which one frightened them most.Here are the top 5 answers from our survey (调查):① Scary movies and TV shows;②Scary dreams;③Thunderstorms,hurricanes(飓风);and other horrible weather;④War and terrorism (恐怖行动);⑤Sounds heard at night.

But not everyone is afraid of the same thing.And what makes one person scared can be of no big deal for someone else.Plenty of kids said their biggest fear wasn’t on our list.

What is fear?

Fear is a feeling that eyeryone has—it’s programmed into all of us—and that’s a good thing because fear is there to protect us.We’re born with a sense of fear so we can react to something that could be dangerous.The baby cries,and their mom comes over to comfort him or her,helping the baby feel safe and OK again.Real vs.Pretend

The best way to get over a fear is to get more information about it.As kids get older,they understand more and start seeing the difference between what is real and unreal.So when William’s imagination leads him to think of witches,he can tell himself,“Wait a minute.They’re only pretend things.I don’t need to worry about them.”

The same goes for the dark.A kid’s imagination can start playing tricks when the lights go out.What’s under my bed?Is that a thief I hear?With the help of a parent,kids can get more comfortable in the dark.Using a nightlight or shining a flashlight under the bed to see that there’s nothing there can help kids fight that fear.

小题1:What did the writer find out from the survey?

A.Some people have never experienced fear.

B.Kids don’t like watching scary movies.

C.All people are afraid of something.

D.People often cry loudly when they are scared.小题2:What is Paragraph 2 mainly about?

A.The list of fears is not complete.

B.The things people fear are of no big deal.

C.Kids have more fears than people think.

D.People are afraid of different things.小题3:In the writer’s opinion,________.

A.having a sense of fear is not a bad thing

B.babies have a weak sense of fear

C.fear is not something that we are born with

D.not all people can react to dangerous things

单项选择题 A1型题