高中数学解三角形习题课：doc全文下载

习题课　正弦定理和余弦定理

一、选择题

1．在△ABC中，若a＝18，b＝24，A＝44°，则此三角形解的情况为                            (　　)

A．无解                                                                              B．两解

C．一解                                                                               D．解的个数不确定

2．在△ABC中，A＝，BC＝3，则AB＋AC的长可表示为                                     (　　)

A．6sin(B－)                                                                      B．6sin(B＋)

C．2sin(B－)                                                                  D．2sin(B＋)

3．在△ABC中，BC＝1，B＝，当△ABC的面积等于时，sin C等于                 (　　)

A.                                                                                B.

C.                                                                                 D.

4．△ABC的内角A、B、C的对边分别为a、b、c，若c＝，b＝，B＝120°，则a等于

(　　)

A.                                                                                    B．2

C.                                                                                    D.

5．若△ABC的内角A、B、C满足6sin A＝4sin B＝3sin C，则cos B等于                (　　)

A.                                                                                  B.

C.                                                                                 D.

6．在△ABC中，若a²＝bc，则角A是                                                                    (　　)

A．锐角                                                                              B．钝角

C．直角                                                                             D．60°

二、填空题

7．在△ABC中，AB＝2，AC＝，BC＝1＋，AD为边BC上的高，则AD的长是________．

8．已知△ABC的面积为2，BC＝5，A＝60°，则△ABC的周长是________．

9．在△ABC中，角A，B，C所对的边分别为a，b，c，若a＝，b＝2，sin B＋cos B＝，则角A的大小为________．

三、解答题

10．在△ABC中，求证：＝.

11.在△ABC中，a，b，c分别为内角A，B，C的对边，且2asin A＝(2b＋c)sin B＋(2c＋b)sin C.

(1)求A的大小；

(2)若sin B＋sin C＝1，试判断△ABC的形状．