山东省济宁市高三数学一轮复?专项训练 解三角形(含解? - 百度文库 ر

12013Ͼ)ǡABCУABԵıֱ߳Ϊab.2asin B3bA ( ) ЦЦЦA. B. C. D. 34612

ڡABCУҶ֪2sin Asin B3sin B BΪABCڽǣsin B0. sin A

3

.֡ߡABCΪΣ 2

??A?0?A.

2?3?

2ڡABCУABCԵı߷ֱΪabca1c42B45㣬sin C______. Ҷbac2accos B13282

42

2

24. 55

2

2

2

2

25b5. 2

sin C

csin Bb 3ڡABCУa23c22A60㣬C( ) A30 B45 C45135 2322

Ҷã

sin 60sin Cãsin C𰸣B

4ڡABCУڽABCĶԱ߷ֱabcab3bcsin C23sin BA

( )

2

2

D60

2

caC60㣬C45. 2

A30 B60 C120 D150

sin C23sin BҶc23b

b2c2a23bcc23bc23bc3

cos A

2bc2bc2bc2

AΪεڽǣA30. 𰸣A

5(2013¿αȫ)ABCڽABCĶԱ߷ֱΪabc֪abcos Ccsin B. (1)B

1

(2)b2ABCֵ (1)֪Ҷ

sin Asin Bcos Csin Csin B AУ(BC)

sin Asin(BC)sin Bcos Ccos Bsin C ɢ٣ںC(0)sin Bcos B.

B(0)B.

4

12

(2)ABCSacsin Bac.

24֪Ҷ

2222

4ac2accos.ac2ac

44

acܣҽacʱȺų

22ˡABCֵΪ21.

6(2013)ڡABCУABCӦı߷ֱabc.֪cos 2A3cos(BC)1.

(1)AĴС

(2)ABCS53b5sin Bsin Cֵ (1)cos 2A3cos(BC)1 2cosA3cos A20

1

(2cos A1)(cos A2)0cos Acos A2(ȥ)Ϊ0AУA. 231133

(2)S bcsin Abcbc53bc20.

2224b5c4.

Ҷabc2bccos A25162021 a21.

Ҷsin Bsin Csin Asin A

2

2

2

2

bacabc22035sinA. a22147

72013ɽ)ABCڽABCԵı߷ֱΪabcac6b2cos B7. 9

2

(1)acֵ (2)sin(AB)ֵ

[淶] (1)Ҷb2

a2

c2

2accos B b2

(ac)2

2ac(1cos B) b2ac6cos B7

9

ac9a3c3(6) (2)ڡABCУ sin B1cos2

B

42

9

(7) Ҷsin A

asin Bb22

3

.(9) ΪacAΪǣcos A1sin2

A13. (10)

sin(AB)sin Acos Bcos Asin B102

27.

(12)

8֪abcֱΪABCڽABCĶԱߣc3asin Cccos A. (1)A

(2)a2ABCΪ3bc. (1)c3asin Cccos AҶ 3sin Asin Ccos Asin Csin C0

sin C0sin???

A?1

6??2

0

6

(2)ABCS1

2bcsin A3bc4.

a2

b2

c2

2bccos Ab2

c2

8bc2. 9ڡABCУa2

c2

b2

3abC( ) A30 B45 C60 D120

a2

c2

b2

3abcos Ca2b2c23ab3

2ab2ab2

C30.

A

10ڡABCУA60㣬AB2ҡABCΪ

3

2

BCijΪ( )

3

A.

3

B.3 C23 D2 2

1133222

SABACsin 60㣽2ACAC1BCABAC2ABACcos 60

22223BC3. B

Ц

11ABCڽABCĶԱ߷ֱΪabc֪b2BCABCΪ( )

64A232 B.31 C232 D.31 Ҷ֪c22

sin Bsin C123226

sin Asin(BC).

222241126

ӶSABCbcsin A22231.

224 B

12(2013)ABCڽABCԵı߷ֱΪabcbcos Cccos Basin AABC״Ϊ( ) Aֱ B C۽ Dȷ

Ҷ֪֪sin Bcos Ccos Bsin Csin Asin(BC)sin ABCУAsin(BC)sin Asin Asin A0AУsin A0sin A1

A.

2 A

13ڡABCУABCԵı߷ֱΪabca2b2sin Bcos B2AĴСΪ________

a?? ֪sin Bcos B22sin?B?2BҶ֪

4?4sin A?

221

ɵãsin AabA. sin Bsin A26

sin

4

6

2

2

2

bcb

1

14(2013̨һģ)ABCڽABCĶԱ߷ֱΪabca1b2cos C

4sin B________

4