8/8/2019 BAI tAP H9

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H thc lng trong tam gic vung

Mt s h thc gia cnh v ng cao trong tam gic vung

I. Kin thc trng tm

1./ AB2 = BH.BC ;

AC2 = CH. BC

2/ AB2 +AC2 = BC2

3/ AH2 = HB. HC

4/ AH .BC = AB . AC

5/1 1 1

2 2 2AH AB AC= +

II. Bi tp

Bi 1. Cho tam gic ABC Gc A bng 900

, AH BC , AB :AC =3:4, BC=15 .

Tnh BH, HC?

Bi 2 .

Cho ABC ,gc A bng 900, ng cao AH. AB : AC =3 : 4 .

AH= 6 cm. Tnh BH,CH

Bi 3.cho tam gic vung cn ABC ( A=900 ; AB=AC )trn AC ly

im M sao cho MC : MA=1: 3 .K ng thng vung gc vi AC

ti C ct tia bm ti K .K BE CK

a) CM : ABEC l hnh vung

b) CM :2 2 2

1 1 1= +

AB BM BK

c) Bit BM =6cm .Tnh cc cnh ca ABC

B

A

H C

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Bi 4. Cho hnh thang vung ABCD ( A D= =900) ng cho BD BC.

BIt AD=12cm ,DC =25cm . Tnh di AB ; BC; BD.

Bi 5.Cho hnh vung ABCD ly E trn BC . Tia AE ct ng thng

CD tai G . Trn na mt phng b l ng thng AE cha tia AD

k AK AE v AK =AE

a/ chng minh K,D,C thng hng

b/ chng minh 2 2 21 1 1

AD AE AC = +

c/ Bit AD =13cm AK : AG =10 : 13

Tnh KG ?

T s lng gic

I. Kin thc c bn1/nh ngha

sin C =

AB

BC ; cos C =

AC

BC

tgC=AB

AC; cotgC=

CA

BA

2/ T s lng gic ca 1 s gc c bit

300 450 600

sin1

2

3

2

3

2

cos 32

2

2

1

2

tg1

31 3

cotg 3 11

3

Trong tam gic vung

*cnh gc vung bng cnh huyn nhn sin gc i (hoc cnhhuyn nhn vi cos gc k )

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*cnh gc vung1 bng cnh gc vung 2nhn vi tg i ( hoccnh vung2 nhn vi cotg gc k )

Bi tp

Bi 1: Chn cu tr li ng nht trong cc cu sau:

1/ Cu no sau ay sai?

A. sin600= cos300 B.tg450.cotg450=1 C. tg150

=cotg850

2/ Bit sin =3/4 vy cos bng

A.1

4B.

5

4C.

3

4D. /S khc

3/Kt qu ca php tnh sin2600+cos2600=

A. 0 B. 1 C. 2 D. . /S khc

4/Kt qu ca sin27015( lm trn n2ch s thp phn)

A. 0,46 B. 0,64 C. 0,37 D. 0,73

5/ Bit sin = 0,1745 vy s o l (lm trn n pht)

A. 9015 B. 12022 C . 1003 D. 1204

6/ Cho bit sin 750=0,966 vy cos150l

A. 0,966 B. 0,483 C. 0,322 D. /S KHC

7/ ABC vung ti A AC =6 ; BC= 12 ; S o ABCbng

A. 300 B. 450 C. 600 D. /S khc

8/ Cc so snh no sau y sai

A. sin450 < tg 450 B. Cos320 < sin320

C. tg 300 = cotg 300 D. Sin 650 = c 250

Bi 2: Cho tam gic ABC vung ti A B=8cm sinC = 0,5.

Tnh t s lng gic ca gc B

Bi 3:Cho ABC AB =40cm ; AC = 58 cm : BC =42cm

1/ ABC c vung khng ? v sao?

2/ K ng cao BH ca ABC.

Tnh di BH( lm trn n 3 ch s thp phn )

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3/ Tnh t s lng gic ca gc A

Bi 4: Cho tam gic ABC vung ti A , AB = a ( a > 0) gc ABC =600

1/ Tnh theo a di AC ; BC.

2/ K ng cao AH ca tam gic ABC .Tnh BH ; CH theo a

3/ Tnh sinC , t suy ra AH.Bi 5: Tnh khong cch gia 2 chic thuyn A v B nh hnh v sau.

Bit rng =370 ; = 100 v IC=150 m

Bi 6: Cho tam gic ABC vung ti A

ng cao AH. BitAB =4cm; gc B=600

Tnh a/ AH; BC.b/ T s lng gic ca g

Bi 7.Cho hnh bnh hnh ABCD c ng cho AC > BD .K CHAD ;

CKAB chng minh

1/ CKH BCA

2/ Chng minh HK =AC. sin BAD

3/ Tnh din tch t gic AKCH bit BAD = 600, AB =4cm , AD =5cm

Gi cu 1.

B1 . cm BCK DCH BC AB

CK CH =

B2. cm KCH ABC = ( cng b vi A )

n tp

Bi 1: Cho tam gic ABC vung ti A ,

ng cao AH. Bit AB =6cm, BH =2cm . Tnh

a/ BC =? AC =? AH =?

b/ ? ?B C= =

Gii : a/ Tnh BC ; AC ; AH.

ABC c AHBCAB2 =BH.BC

AD

CB

K

H

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BC =2

3618

2

AB

BH= =

AC = 2 218 6 288 12 2 = =

AH. BC = AB. AC AH =6.12 2

4 218

=

b/ Tnh ; ?B C =

ABC vung ti A c sinC =12 2

180,9428 C 700 32

M B C+ = 900 0 089 60' 70 32'B = =19028

Bi 2: T s hai cnh gc vung ca tam gic vung l 5 : 12 . dicnhk huyn l 39 cm .Gii tam gic vung y

Gi :2 2 2 2 2 2

5 39

12 5 12 25 144 169 169 169

b b c b c b c a

c

+= = = = = =

Tnh b; c ;t tnh gc B; gc C

Bi 3: Cho tam gic ABC c AB = 16cm; AC =14 cm ; gc B bng 600

a/ Tnh BC

b/ Tnh din tch ABCGi : K ng cao AH ;Tnh AH; BH trong tam gic

Vung AHB; Tnh HC trong tam gic vung AHC

T suy ra BC ; Din tch tam gic ABC

Bi 4: Cho tam gic vung ABC , vung ti A,Phn gic AD, ng cao AH. Bit CD = 68cm

BD =51cm .Tnh HB , HC

Gi

Vn dng t/c ng phn gic ta c

2 2 2 2 2 2

2 2

119

68 51 7225 7225 722568 51

b c b c b c a+

= = = = =

Tnh c AB; AC. T tnh c HB; HC.

Bi 7 Khng dng bng s hay my tnh .Hy tnh

B

A

CH

A B

C

HD

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a/ A = 4cos2 -6sin2 Bit sin = 0,2

b/ B = sin .cos Bit tg + cotg =3

c/ C = cos4 -cos2 +sin2 Bit cos = 0,8.

Bi 8: Cho tam gic ABC c AB =6cm; AC =4,5cm ; BC =7,5 cm

a/ Chng minh tan gic ABC vung

b/ Tnh ;B C; ng cao AH

c/ LyM bt k trn BC .Gi hnh chiu ca M trnAB;AC l P;Q.Hi M v tr no th PQ c di nh nht .