-
202
åºæ¬ äŸé¡ 124 äžè§åœ¢ã®æå€§è§
B/1
00000
â³ABCã«ãããŠ,次ãæãç«ã€ãšãããã®äžè§åœ¢ã®æã倧ããè§ã®å€§ããã
æ±ããã
a b C
(1) 3-188=1X
7 X (2) sin A: sin B: sin C=1: â2: â5
p.194 åºæ¬äºé
åºæ¬121
CHART & SOLUTION
åºæ¬ äŸ
â³ABC
(1) 蟺
(2) 4
CHA
äžè§åœ¢ã®èŸºãšè§ã®å€§å°é¢ä¿
a <bâA<B æå€§èŸºã®å¯Ÿè§ãæå€§è§
æ¯äŸåŒã¯ãšãã, a, b, c ãk ã§è¡šããŠäœåŒŠå®çãå©çšã,
è§ã®å€§ãããæ±ããã
å°
+
äžè§
蟺
B
(1) a>b>c ã§ãããã, æå€§èŸºã¯BC ã§æå€§è§ã¯â Aã§ããã
C
ãã!
a b C
(1) 13-18-1 ã®å€ãk (k>0) ãšãããš
7
a b C
Ninf.
ã®åœ¢åŒ
(1
x y Z
a=13k, b=8k,c=7k
7k
8k
ãæ¯äŸåŒãšããããªããããªã?
蟺BCãæå€§ã®èŸºã§ãããã,ãã®
察è§ã® â A ãæå€§ã®è§ã§ããã
ãã®æ¯ã®é¢ä¿ã
æŽç
B
13k
C
a:b:c=x:y:z
å
±é
äœåŒŠå®çã«ãã
ãšæžãããšããã,ãã®ãš
(2)蟺
+8
ãã®Î±: bc ã
cos A=
(8k)2+(7k)2-(13k)2
2.8k-7k
-56k²
1
a,b,cã®é£æ¯ãšããã
ã
2.8.7k2
2
ãã£ãŠ, æå€§ã®è§ã®å€§ãã㯠A=120°
DOS
[1]
7
(2) æ£åŒŠå®çã«ãã
a: b:c=sin A: sin B: sin C
ãã£ãŠ a:b:c=1:â2:â5
ããã«,k(k> 0) ãçšããŠ
inf. æ£åŒŠå®çãã
A
sinA=-
a
2R'
sin B=-
2R'
â5k
[2]
C
â2k
|sinC=
2R
Bk C
ãããã£ãŠ
a=k,b=â2k,c=â5k
ãšè¡šããããã,蟺AB ãæå€§ã®èŸºã§, ãã®å¯Ÿè§ã®â Cã
æå€§ã®è§ã§ããã
sin A sin B: sin C
a
b
2R 2R 2R
C
:
äœåŒŠå®çã«ãã
=a:b:c
cos C=-
k2+â2k2-(â5k)2-2k
2.k.â2k
1
==
2â2k2 â2
ãããã£ãŠ, æå€§ã®è§ã®å€§ããã¯
C=135°
PRACTICE 124
â³ABCã«ãããŠ, sin A: sin B: sinC=5:16:19 ã®ãšã,ãã®äžè§åœ¢ã®æã倧ã
éã®å€§ãããæ±ããã
Po
P