C. CAU HOI VA BAITAP
b) Tfnh dtrdng ca ob xuat phat tir dinh Ava ban kfnhR cCia dudng trdn
GlAl
a) Theo dinh If cdsin ta cd
a2=fe2+c2_2feccosA = 7^+5^-2.7.5.- = 32 =>a = 4V2 (cm) 5
. 2 2 9 16 4 sm A = l-cos A = l = — =>sinA = —(vi sinA >0).
25 25 5 5 = -fecsinA = - . 7 . 5 . - = 14 (cm^). 5 = -fecsinA = - . 7 . 5 . - = 14 (cm^). 2 2 5 . - , 2.5 28 7V2 , , b) h = — = —7= = (em). '' a 4V2 2 ' '
Theo dinh If sin: - ^ = 2R => R = —^— = ^ = ^ (cm).
sinA 2sinA 2 I 2
Vi du 2. Cho tam giac AfiC biet A = 60°, b = 8 cm, c = 5 cm.
Tfnh dudng cao b^ va ban kfnh R ciia dudng trdn ngoai tiep tam giac AfiC.
GIAI
2 2 2
Theo dinh If cdsin taco : á =b +c - 2bc cos A
= 8^+5 -2.8.5.cos60°= 49. vay a = 7 (em).
Theo cdng thiic tinh dien tfch tam giac S = — fee sin A, ta cd
S = -.8.5.sin60° = - . 8 . 5 . - ^ = 10>/3 (cm^). 2 2 2 o 1 , , 2S 20V3 , , Mat khac S = -ạh^ ^ h= — = ^ (cm). 2 " . " a 1 , , ^ abc , „ abc 7.8.5 iS , ,
Vi du 3. Tam giac AfiC cd Afi = 5 cm, fiC = 7 cm, CA = 8 cm. a) Tfnh Afi .AC ; b) Tfnh gdc Ạ
GIAI
a)TacdBC =(AC-ABy =AC + AB -2AC.AB.
Dođ AC.AB = - AB +AC -BC = - ( 5 ^ + 8 ^ - 7 ^ ) =20.
2 vay AC.AB = 20.
b) Theo dinh nghia : AB. AC = I AB| . | Ac| cosẠ Ta cd :
JB.JC 20 1
cosA =
AB.AC 5.8 2 vay A = 60°.
Vi du 4. Cho tam giac AfiC biet a = 21 cm, b = 17 cm, c = 10 cm. a) Tinh dien tfch S cua tam giac AfiC va chieu cao b^.