C D= 7AI3 ^+ (A D Bf = ^•
DE =—= a,De thay ASAI ~ ADEI ^
De thay ASAI ~ ADEI ^ - -
SA SI a77 77 77 V
BD 1 (SAD) => BD 1 DE . Trong tarn giac vuong BDE ta c6 : t a n B ^ = - ^ = ^ =DE 4 V7 t a n B ^ = - ^ = ^ =DE 4 V7
=>BED = âctan^/7
Vay ((SAD),(SBC)) = arctan ^7 2) Dung A P 1 S H , P € S H .
Do C D l ( S A H ) r ^ A P l C D ^ A P l ( S C D ) . Tuong tu, dung A Q 1 SC,Q e SC
thi AQ 1 (SBC).
Do do PAQ = ((SBC),(SCD)). Trong tam giac SAH ta c6 :
1 1 1 ' 1 1 ^ 1 '
Ap2 AS^ AH^ - + •
D l thay ASAC vuong can tai A nen AQ = ^ S C = = ^ , Do A P 1 (SCD) ^ A P 1 P Q .
Trong AAPQ c6 cosAPQ = AP _ ^is^^ VlO
AQ aVe 5 APQ = arccos Vio
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Cty TNHH MTV DWH Khang Viet
Vay ((SBC),(SCD)) = arccos Vio
X?i du 2.2.8. Cho tam giac ABC c6 AB = 3a , duong cao CH = a va A H = a nam trong mat phang (P). Tren cac duong thang vuong goc voi (P) ke tu
A,B,C Ian luot lay cac diem Á,B',C' tuong ung nam ve mot phia ciia (p) sao cho AAj = 3a,BBj = 2a,CCj = a . Tinh dien tich tam giac A ' B ' C .
Xffi gidị Ta CO SABC = 3â Vi CH 1 AB,CH = a, AH = a => AC = a>y2 va BAC = 45". Goi I = B'C'nBC,J = A ' C ' n A C . Taco C C ' - i B B ' ^ B C = CI 2 C C = i A A - = ^ C J = l A C = ^ . 3 2 2
Xet ABCH ta c6 BC^ = BH^ + CH^ = Sâ ^ BC = aVs
Mat khac AB^ = CÂ + CB^ - 2CẠABcosC
= > C 0 S C = : -C A ^ + C B ^ - A B ^ 1
2CẠCB 10
Xet AICJ ta c6 IJ^ = C P +CJ^ -2CỊCJcosICJ = 26á ft.'!,-
Ke duong cao C K cua A I C K , do C C 1 (iCj) nen C ' K 1 I J .
Vay C " ^ chinh la goc giua hai mat phang ( A B C ) va ( A ' B ' C ' ) n e n
•'ABC = S A . B ' C ' ' ^ o s C ' K C . T a CO Sjcj = | S A B C
Mat khac S^q = ^IJ.CK => CK =
3â
_ 2Sicj _ 2 _ _ 3a IJ V26a N/26 ' Xet AC'CK taco tanC'KC = C C ' ^ a
CK ~ Jâ V26 V26
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Phuwig phap giai Toan Hinh hgc theo chuyen de- Nguyen Phu Khdnh, Nguyen TS^ Thu
Ma l + tan^C'KC = 1 •cosC'KC =
cos^C'KC V35
Vay SABC = S A ' B ' C COSC'KC => S^.B^C = " 'ABC
cosC'KC 2 ' • C a B A I T A P
Bai 2.2.1. Cho hinh chop S.ABC c6 day ABC la tarn giac can tai A, AB = a va SA 1 (ABC). Mat phang (SBC) tao voi day mot goc 60" . Goi M , N Ian luot la trung diem cua SB va AC. Tinh :
1) Co sin ciia goc giiia hai mat phang (SAC) va (SBC)