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问题 填空题
如图，在底面边长为2的正三棱锥V-ABC中，E是BC的中点，若△VAE的面积是
1
4
，则侧棱VA与底面所成角的大小为arcsin
3
12
．（结果用反三角函数值表示）
答案

在正三棱锥V-ABC中，E是BC的中点；

∴VA与底面所成角是∠VAE；

∵△VAE的面积是

1
4
，∴
1
4
=
1
2
VA•AE•sin∠VAE；

∵正三棱锥V-ABC的底面边长为2，∴AE=

3
，∴VAsin∠VAE=
3
6
；

即三棱锥的高为

3
6
，又顶点在底面上的投影是底面的中心，令为O，则AO=
2
3
3

∴VA=

(AO)2+(VO)2
=
(
3
6
)2+(
2
3
3
)2
=
17
12

∴sin∠VAE=

3
6
VA
=
3
6
17
12
=
1
17
=
17
17
，则所求的角为arcsin
17
17
；

故选Arcsin

17
17
．

填空题

B Customs of Bulgaria: Marriage and Family保加利亚习俗：婚姻与家庭
The average age for women to marry is between 18 and 25.25 tend to (1) when somewhat older. A church wedding often (2) the legal civil ceremony, and a large reception, which often involves (3) music and dancing, is held in the evening. Wedding traditions include (4) money on the bride’s dress to represent future prosperity, the groom (5) the bride at her home, and the couple pulling on opposite (6) of a loaf of bread—whoever gets the largest piece will be (7) boss of the family. Honeymoons are a new tradition.
The principle (8) mutual support is valued in the Bulgarian family. The elderly are (9) cared for by their adult children. Unmarried adults live with their (10) and many newly married couples live with one set of parents (11) they are able to get housing of their own. Most families (12) urban areas live in apartments, which are in short
supply, while (13) in rural areas usually have their own houses. Many village houses (14) owned by families who live in urban areas, who use them_ (15) summer and weekend retreats, or for retired parents.
Most families in (16) areas do not have more than two children, while families in (17) areas tend to be larger. Grandparents play an important role in (18) care, particularly in urban areas, where most women work outside the (19) . Men of the younger generation have begun to help with household (20) , once considered only women’s responsibility.

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翻译题

完成句子。

1. ______________, (为了通过考试) he stayed up late preparing for it. (order)

2. It was the second time that ______________. (他给我打电话) (telephone)

3. Finally we ______________ (完成这项任务), although it took a long time. (get)

4. It was a burning cigarette end _____________ (引起火灾) in the city. (cause)

5. People who listen to Hawking's lectures sometimes ______________.(发现很难理解他) (find)

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