IRAN VINH HINH HOC TAP HAI • II NHA XUAT BAN HA NOI ^ • TRAN VINH THIET KE BAI GIANG I l I M l IKN J NANG CAO - TAP HAI NHA XUAT BAN HA NOI LflflNOIDAU Bit diu tii nam hoc 2006 - 2007, hai bo sach giio khoa toan moi : Co ban va Nang cao da duoc su dung tren toan quoc Viec thay sich luon gin liin v6i viec ddi mofi phuong phap day hoc Bo sach Thiet ke bai giang Toan 10 - nang cao ddi nhim phuc vu viec ddi moi Bo sach dugc bien soan dua tren cac chuong, muc cua sach giao khoa, bam sit noi dung ciia sich giio khoa, tijr hinh nen cau true mot bai giang theo chuong trinh m6i: Lay hoc sinh lam trung tam va hd trg ciia cac phuong tien day hoc hien dai Phin dai sd gdm tap Tap T gdm cic chuong 1, chuong II va chuong 111 Tap : gdm cac chuong IV, chuong V va chuong VI Phan hinh hge gdm tap Tap 1: gdm chuong I va bai 1, bai chuong II Tap 2: phan lai Mdi chuong dugc thiet ke cong phu, dua cac cau hoi va tinh huong thu vi Trong cac boat dgng chiing toi co' ging chia lam pljin:' Phin cCia giao vien (GV) va phin ciia hge sinh (HS), mdi phin co cac cau hoi chi tilt va hudfng din tra ldi Thuc hien xong mdi boat dgng, la da thuc hien xong mgt don vi kiln thiic hoac cung co' don vi kie'n thiic Sau mdi bai hge chiing toi co dita vao phin cau hoi trie nghiem khach quan nhim dl HS tu dinh gii dugc miic nhin thiic va miic tie'p thu kiln thiic ciia minh Sau mdi bai chiing toi cd ging co nhiing phin bd sung kiln thiic danh cho GV vaHS gioi Phan phu luc dai so la phan danh cho giao vien, nhim sii dung cac phin mem cua toan hge lam chii kien thiic, lam chu cac so cin tinh toan tir neu len dugc each day moi chii dgng va sang tao Day la bg sach hay dugc tap the tie gia bien soan cong phu, iing dung nhiiu tuu khoa hge moi tinh toan va day bgc Chiing toi hy ygng dap iing dugc nhu cau cua giao vien toan viec ddi moi phuong phap day bgc Trong qua trinh bien soan, khong the tranh khoi nhiing sai sot, mong ban dgc cam thong va chia se Chiing toi chan cam on su gop y ciia cac ban Tac gia Chi/dNq II HUdNG CUA HAI VEC TO VA LfNG DUNGCtiep theo) TICH V O §3 He thu'c liidng t r o n g t a m giac (tiet 5, 6, 7, 8) MUCTIEU Kien thurc HS nim dugc: Dinh li cosin, dinh li sin tam giac va cac he qua Cac cong thiic tinh dai trung tuyin va dien tich tam giac Hge sinh van dung dugc cac cong thiic tren de giai cac bai toan chung minh va tinh toan co lien quan din dai trung tuyin, dien tich, chieu cao ciia tam giac KT nang • Van dung thao dinh li cosin va dinh li sin de tinh cac goc, cac canh chua bie't ciia tam giic da biet ba canh hoac hai canh va goc xen giira, hoac mgt canh va hai goc kl Thai • Lien he dugc voi nhiiu van dl co thuc te , nhat la dac • Co nhiiu sang tao hinh bgc • Nhan thirc to't hon tu hinh hge n CHUAN BI CUA GV VA H6 ' Chuan bi cua GV: GV: Chuin bi mgt so' cac vi du da hge a lop de dat cau hoi Chuin bi mgt so' hinh sin d nha vao giay hoac vao ban meca de chiiu neu co miy chiiu: Tur hmh 44 de'n hinh 58 Chuin bi phin mau Ngoai phai ve sin mgt so' hinh 6i hudng din bgc sinh thuc hien cac" Chuan bi cua HS : • Dgc bai ki d nha, co the dat cac cau hdi vl mgt van 6e ma em chua hieu • Chuin bi tdt mdt so cdng cu de ve hinh m PHAN P H O I THCDI LUONG Bdi ndy chia ldm tiet' Tiet 1: tit ddu den het phdn (dinh li sin); Tiet Mtic 3, Tiet Muc 5(gidi tam gide) Tiet On tap IV TIEN TDINH DAY HOC n KiCMTRn Bi^lCU GV: Kiem tra bdi cd 5' Cau hoi •Cho tam giac vudng ABC, vudng tai A, BC = a = 60'' a) Tinh cic gia tri lugng giic cua cic gdc tam giic b)Tinh AB.BC; AB.CB; AB.CA Cau hdi Cho tam giic ABC, A(l ; 1), B(-2; -1), C(3; -2) a) Tinh cac gdc tam giac; b) Tinh AB.BC; AB.CB; AB.CA B iini M I nOATDONGl L Dinh li cosin tam giac a) Muc dich: Giiip HS biit dugc dinh 11 cdsin va biit van dung nd giai toan b) Hudng thifc hien - Ddt van de - Thue hiin - Thite Men -^f - Niu dinh li odsin - Thuc hiin / \ - Thue hiin J ^ - Hudng ddn HS ldm vi du trang 54 SGK, vi du trang 55 - Niu chii y quan trgng c) Qud trinh thifc Men • Dat vin dl GV ve hinh 44 len bang ^ C Hmh 44 - Cho mdt HS phit bieu dinh li Py - ta - go cho hinh 44: BC^ = AC^ AB' - Phin tich fiC = AC - A6 Tir ta cd BC =(AC-AB)^=AC + AB^-2AC.AB = AC^+Jf^ • Thuc hien ?1 GV: Thi/c hien thao tac 2' Hoat dong cua giao vien Cau hoi Hoat dgng ciia hoc sinh Ggi y tra ldi cau hoi Trong chiing minh tren, A vudng Vi A vudng , nen AC L AB, hay dugc su dung budc nao? Z6.AC = Cau hoi Ggi y tra Idi cau hoi NIu bd di gia thiet A vudng thi Khdng diing kit luan tren cdn diing hay khdng? • Thuc hien ^ C GV: Thu'c hien thao tac 5' Hoat dgng ciia giao vien Cau hoi Hoat dgng cua hoc sinh Ggi y tra Idi cau hoi Hay phan tich BC theo AB vh 'BC = Jc Ggi y tra Idi cau hoi Cau hoi Hay tinh BC Cau hoi 'BC = JC JC-JB = (AC - Afi)2 +~AB -IAC.JB Goi y tra Idi cau hoi Hay ip dung dinh nghia tich vd hudng cua hai vecto trudng AB.AC = AB.AC cos A hgp Ggi y tra Idi cau hoi Cau hoi Kit luan a = b2 + e2 - IbecosA GV thifc hien thao tac 3' Hoat ddng cua giao vien Hoat ddng cua hge sinh Cau hdi Ggi y tra ldi cau hdi Khi nao thi M nim tren A? Khi Cau hdi TM = tu Ggi y tra Idi cau hdi Tim toa ciia IM /M = ( x - x o ; y - y o ) - Cau hdi Ggi y tra Idi cau hdi Tim toa ciia t.u t.u = (ta;tb) Cau hdi Ggi y tra Idi cau hdi So sanh toa cua hai vecto tren rdi kit luan r x-A'o = at [y-yo^bt Tii boat ddng tren suy diiu kien dl M(x ; y) thudc A la cd sd /• cho X = Xn + ta " y = yo + tb T o (a2 +b^ ^ 0) (1) He (1) dugc ggi la phuong trinh tham sd cua dudng thing A, vdi tham sd t GV dat cac cau hdi de hge sinh tra ldi HI: Mdt dudng thing cd bao nhieu vecto chi phuang? H2: Cac vecto chi phuong cua mdt dudng thing cd quan he vdi nhu the nao? H3: Khi bill phuang trinh tham sd ciia mdt dudng thang ta cd mdt diem thudc dudng thing Dd la diem nao? 84 Chii y' Vdi mdi gia tri cua tham sd t, ta tfnh dugc x va y tit he (1), tiic la cd dugc diem M(x ; y) nim tren A Ngugc lai, niu diem M(x ; y) nim tren A thi cd mdt sd t cho x, y thoi man he (1) Thuc hien ?3 GV thifc hien thao tac 5' Hoat ddng ciia giao vien Cau hdi Hoat ddng ciia hge sinh Ggi y tra Idi cau hdi Cho dudng thing A cd phuang trinh tham so A: H = (l;-2) fx = + r \y = \- It a) Hay chi mdt vecto chi phuang ciia A Cau hdi Ggi y tra Idi cau hdi t=0, M(2;l), Tim cic diim cua A iing vdi cac t= -4, M(-2 ; 9) gii tri t = 0, t = - 4, t = - t4,M(f;0) Cau hdi Ggi y tra Idi cau hdi c) Diem nao cic diim sau Diim (XQ ; yo) e A va chi cd t fxo=2 + t thudc A ? cho M(3;2) a) Hay tim toa cua mdt diem thugc d va viet phuang trinh tham sd ciia d Cau hdi Ggi y tra Idi cau hdi 2 'x = + 1,5/ Trudc hit xem A(2; — ) cd thudc d He • cd la phuang hay khdng? trinh tham sd cua d khdng ? Thay vao ta thiy A e d Han niia u'(\,5;\) ciing hudng vdi u nen nd la vecto chi phuong cua d Vay phuang trinh tren la phuong trinh tham sd cua d Cau hdi Ggi y tra Idi cau hdi Tim toa ciia diem M thudc d Diim M thudc d nen M = (3 + 3t ; 2t) cho OM = (theo a) OM = (3 + 3t)2 + (2t)^ = [...]... = 18 0° - (A + B) « 57° c) c^ = a^ + b^ - 2ab.cosC = 7" + 23^ - 2.7.23.cosl30° « 784,98 Suy ra c « 28,0 a.sinC 7.sin 13 0° ^,r.,^ , sinA = — * w 0 ,19 15 c 28 Suy ra A ~ 11 °, B = 18 0° - (A + C) * 39° Bai 35 Hudng dan ^ ^ b2+c2-a2 18 2+202-I42 ^ o a) cosA = * w 0,7333 =i> A = 43 2bc 2 .18 .20 Tuo'ng ty tfnh dugc B ~ 61 Cd the tfnh : ^ b.,sinA 18 .sin 43° ^ „^,^ smB = « ~ 0,8769 a 14 Suy ra B * 61 , C ~ 18 0°... thifc Men Bai -15 Hoat ddng ciia giao vien Cau hdi 1 Hay ip dung dinh li cdsin tfnh Hoat ddng ciia hoc sinh Ggi y tra Idi cau hdi 1 cosA Cau hdi 2 Thay sd va tinh toan cosA = b2+c2-a2 2 be Ggi y tra Idi cau hdi 2 cosA = 13 ^ +15 ^ -12 ^ 0,6 410 2 .13 .15 Suy ra A * 50° Bai 16 Hudng din HS ip dung dinh If ham sd cdsin a^ = b^ + c^ -2bc cosA = 5" + 8" -2.5.8 cosdO'' = 49 Vdy a = 7 Kei qud b) diing Bai 17 Hoat ddng... o c) B = 20 a= c.sinA = 35.sin40° sinC sin 12 0° c sinB 35.sin20° = b= sinC , ^ , ~ 26,0 \a * 13 ,8 sin 12 0° d) A = 40° b= a.sinB = 13 7,5 sin 83° sinA va c= -,,,.,,, K 212 ,3 sin 40° a.sinC sin A = 13 7,5.sin57° ,_ , ~ 17 9,4 sin 40° Bai 34 Hudng dan a) A = B = (18 0° - C) : 2 = (18 0° - 54°) : 2 = 63° Canh c cd the tfnh theo dinh li sin hoac cosin : 3-TKBG HH 10 - NC-T2 33 a.sinC c= 6,3.sin 54° = sinA _„ «... tinh kit qua gin diing CH = AC • Neu chii y 14 16 9,4 13 4,7 (m) , , , 70.sinl05''30' ^ ^, Neu sii dung MTBT de ti'nh bieu thuc b = thi ta co the sinl4°30' lim nhu sau 1) Dd'i vdi MTBT CASIO/x-220 hoac/x-500A thi an [( 10 5 o,,, 30 o,,, .)] 0 EJ sin 14 o,., 30 o,., .)] [il.Kltqua:Z? « 269,4 2) Dd'i vdi MTBT CASIO/x-500MS thi an 70 0 [sin] 10 5 0 ^ 30 0 ^ 0 |sin| 14 O''' 30 Oi'y 0 Kit qua:b ~ 269,4 • Thuc... CA + AB) = pr • Thuc hien ^ ^ 10 GV thu'c hien thao tac nay trong 2' Hoat ddng ciia giao vien Hoat ddng cua hge sinh Ggi y tra Idi cau hdi 1 Cau hdi 1 Hay tinh dien tich tam giac cd 3 S=6 canh 3, 4, 5 Ggi y tra Idi cau hdi 2 Cau hdi 2 S= 84 Hay tinh dien tfch tam giac cd 3 canh 13 , 14 ,15 Cau hdi 3 Ggi y tra Idi cau hdi 3 Hay tinh dien tfch tam giac cd 3 S =11 70 canh 51, 52, 53 HOAT DONG 5 5 Giai tam... « 18 0° - (10 1 °2' + 47°20') = 31 38' • Thuc hien vf du 7 A,^ - Cho HS thao luan dl bai J-^^'^^ - Ve hinh 56 5-==— ^ \ =— —^C Hinh 56 Day la bai toan thuc te, GV hudng din hge sinh lam bai theo cac budc sau day: - Tinh gdc A dua vao dinh II ham sd cdsin; - Ap dung dinh If ham sd sin, tinh cac gdc B va C - Chii y : nen diing may tfnh bd tiii dl tfnh kit qua gin diing Ket qud B ~ 28°38' ; C 18 0° - (11 7°49'... 2 A 7 ( 7 C + 7 B ) = 2 A 1 ' + 2IC^ 2 AB^ + AC^ =ln? +— 2 ^ • Giai bai toan 2 - Cho HS neu va thao luan vl bai toan - Goi mdt HS ve hinh 51 - Ap dung bai toin 1: ta tfnh MP^ + MQ^ theo a va k ,2 Ket qua: Ml 2 = 2 4 • Thuc hien^%^ 6 GV: Thi/c hien thao tac nay trong 4' 2-TKBGHH10-NC-T2 17 Hoat ddng ciia giao vien Hoat ddng eiia hge sinh Cau hdi 1 Ggi y tra Idi cau hdi 1 Hay nhan xet ve (*) VI trai... COB + AOB = 18 0° nen sin COB = sm AOB Vay S| + S, = - OB.(AO + OO.sin AOB = - OB.AC sin AOB 1 Tuong tu : S3 + S4 = - OD AC.sin AOD Lai cd sin AOB = sin AOD 32 , nen S, + S2 + S3 + S4 = - AC.(OB + OD)sm AOB = - AC.BD.sin AOB Bai 33 Hudng din a) Ta cd C =18 0° - (A + B) = 18 0° - (60° + 40°) = 80° a sin A => b = csinB = I4.sin40° sinC b c sin B sin C ^, csinA 14 .sin60° * 9 ,1 va a = = »= 12 ,3 sin 80°... ciia giao vien Cau hdi 1 Hoat ddng ciia hoc sinh Ggi y tra Idi cau hdi 1 Hay tfnh h^ trong tam giac AHB h^ = csinB theo canh c va gdc B Cau hoi 2 Ggi y tra Idi cau hdi 2 Thay vao cdng thiic 5 = -ah^ de dugc cdng thiic (2) S = —ali^ = —acsinB 1 " 1 •Thuc hien S ^ 8 GV thu'c hien thao tac nay trong 2' Hoat ddng cua giao vien Cau hdi 1 Hoat ddng ciia hoc sinh Ggi y tra Idi cau hdi 1 Hay tfnh sinC tu' dinh... tinh bd tiii ta tinh dugc A « 16 °58' • Neu chu y: Hudng din HS thuc hanh ngay cic bai tap tren Neu su dung may tinh bd tiii (MTBT) dl tinh gdc A khi biet cos A = 0,9565 ta cd thi lam nhu sau 1) Dd'i vdi MTBT CASIO/x-220 hoac/x-500A thi an 0.9565 SHIFT cos SHIFT Ol'' Kit qui : A =* 16 °58' 2) Dd'i vdi MTBT CASIO/x-500MS thi in SHIFT cos 0.9565 0 O' ? 5 Kit qua : A ~ 16 "58' 11 HOAT DONG 2 2 Djnh li sin ... Viy ciy cao 17 ,4 m Bai 38 Hudng din Tam giic ABC cd A = 50° - 40° = 10 va B = 90° - 50° = 40° .^ , a.sinB 5.sin40° AC = b = = % 18 ,5 SinA sin 10 CD = AC.sin40° « 11 ,9 ^ CH « 11 ,9 + = 18 ,9 (m)... hdi cosA = 13 ^ +15 ^ -12 ^ 0,6 410 2 .13 .15 Suy A * 50° Bai 16 Hudng din HS ip dung dinh If ham sd cdsin a^ = b^ + c^ -2bc cosA = 5" + 8" -2.5.8 cosdO'' = 49 Vdy a = Kei qud b) diing Bai 17 Hoat ddng... b2+c2-a2 18 2+202-I42 ^ o a) cosA = * w 0,7333 =i> A = 43 2bc 2 .18 .20 Tuo'ng ty tfnh dugc B ~ 61 Cd the tfnh : ^ b.,sinA 18 .sin 43° ^ „^,^ smB = « ~ 0,8769 a 14 Suy B * 61 , C ~ 18 0° - 43° - 61