问题 解答题
已知△ABC的三个内角A,B,C所对的边分别为a,b,c,∠A是锐角,且
3
b=2a•sinB.
(Ⅰ)求∠A的度数;
(Ⅱ)若a=7,△ABC的面积为10
3
,求b2+c2的值.
答案

(Ⅰ)∵

3
b=2a•sinB,

∴由正弦定理知:

3
sinB=2sinAsinB,

∵∠B是三角形内角,

∴sinB>0,

∴sinA=

3
2

∴∠A=60°或120°,,

∵∠A是锐角,

∴∠A=60°.

(Ⅱ)∵a=7,△ABC的面积为10

3

∴10

3
=
1
2
bcsin60°,

∴bc=40;

由余弦定理得72=b2+c2-2bccos60°,

∴b2+c2=89.

单项选择题
阅读理解

阅读理解。

Columbus College, 241 Queen Elizabeth Drive, Kowloon City

   To: All Staff

   From: Jakie Mok, Secretary; Sports Development Committee

   Date: May 20, 2010

   A Week ago, "Sports for Life" programme was sent to the parents, requiring them to select a sport

they wanted their child to play. Since then, our staff have received lots of calls from parents asking for

more information about it. Here is a memo (备忘录) for your reference when you answer the phones:

   Sports 1: Basketball

   We expect that this will be the most popular of the four sports. Therefore, students should be advised

to sign up as soon as possible. Students will take a private bus to and from Kwun Tong Sports Park. To

cover the cost of hiring a bus, each student will have to pay $10 each time. There will be four basketball

courts available for our use with one teacher watching over each game.

   Sports 2: Gym

   We will be using St. Peter's Memorial Park. There are two reasons for choosing this park. First, it is

not very busy and crowded before 6:00 pm. Second, it has a lot of trees with plenty of shade. Students

must bring along two bottles of water to prevent thirst. Three activities, skipping, jogging, outdoor

aerobics (有氧运动), all of which are free of charge, will be arranged. And there will be a teacher on

duty for each of the activities.

   Sports 3: Hiking. (远足)

   Hiking will take place at Kowloon Peak. The activity will start at 2:30 pm and finish 90 minutes later.

Three teachers will accompany the students, and a hiking instructor will accompany each group of 15

hikers. Each instructor will cost $ 75/hr.

   Sports 4: Swimming

   The Kowloon City Aquatic Centre is a 10-minute walk from our school. Four teachers will go to the

pool and conduct the goings-on from the poolside. We will only be able to reserve the pool for one hour

(i.e. 2:45pm to 3:45pm). Only students skillful at swimming can take up this activity. The pool will have

two lifeguards present. Girls must wear a swimming suit. The cost is $10 per visit.

1. Which of the following is TRUE according to the passage?

A. Students selecting basketball had better register early.

B. Students participating in gym should arrive at 6:00 pm.

C. Hiking usually begins at 2:30 pm and lasts 2 hours.

D. Students having swimming suits can take up swimming.

2. It can be inferred from the passage that ________.

A. students taking part in basketball will walk to the courts

B. every student can gain admission to one of the four sports

C. hiking students can have a regular rest in the shade of trees

D. students taking up the four sports should bring bottles of water

3. It can be concluded that ________.

A. each sport will take only an hour

B. students will be charged for the four sports

C. all the sports will take place at Kowloon Peak

D. teachers will accompany students on each sport

4. The purpose of the memo is to ________.

A. attract students' interest in the programme

B. require the parents to select a sport for their child

C. help the staff explain the programme to the parents

D. remind teachers and lifeguards to be present on time