ޤ̾ܤʤΤǡޤƤʤ褦Ǥ
ΤᤤȤʤ褦Ǥ
ǰʤʾС
423ڡ 0:09:41 48977
ߤ
£ģäѷ£ģФࡣ
λȾʬˤľջѷ£äͿ줿ޤˤʤ롣
423ڡ 0:13:40 48978
algebra
ABaBPx Ȥȡꡤx/sin302a/sin135
ꡤxaäơAPB(18030)/275
423ڡ 0:21:20 48980
Ȥ
ɸA(0,0),B(1,0),C(0,1)Ȥ
ľCA:-(2+sqrt(3))*x+1
ľBP:y=-sqrt(3)*(x-1)/3
2ľθP
tan(PAB)=Pyɸ/Pxɸ
XMaxima ǵ

part(solve([y=-sqrt(3)*(x-1)/3,y=-(2+sqrt(3))*x+1],[x,y]),1)$
rat(factor(rhs(part(%o1,2))/rhs(part(%o1,1)))),algebraic;
2+sqrt(3)
tan(PAB)=2+sqrt(3)PAB=75
APB=180-75-30=75롦()
˭ԡ 423ڡ 0:23:40 MAIL:fttnm528@ybb.ne.jp 48981
٥륯åĥ
AB=APAP=PCȤȳΤˤηˤʤꡢ75٤ʤΤϴְ㤤ʤΤǤȤˡϤޤפĤޤ

䤪ޤ󤵤
ȤꤢåȤʤФȤȤʬޤ
μǤϤʾʬޤ
ĶWIN10ѤˤϤޤIEȤäƤޤ
423ڡ 0:38:36 48982
⡼ޥ
BC=2 ľ¤ȤߤCPȤθQȤ...
QBPϾľջѷǤơ
AP=2
AB=2/2=2
so...AB=AP
so...(180-30)/2=75

...8/5ǤʤޤޤǤäƤߤ̾ܤޤ..^^; Orz
423ڡ 0:42:56 48983
Ȥʤ
᡼硢ʤɤϷޤäƤǤ礦
ϹäƤϤʤΤ˽ɽ˺ܤޤǤ
423ڡ 0:53:48 48984
ǯ
#48978ߤ󤵤ƱǤ
η˥եåȤơ1ĤʤȤȽΤǤ
ȤǤʤջѷ3015뤫ˡϡ
423ڡ 2:48:06 48985
ֿء׾ι
Ȥꤢľǡ
423ڡ 6:47:18 48986
̴
BPαĹACθDȤȡABDϢAľѤǤΤǡ
ľ¤BDȤߤܤ롣ʬBCαߤȤθEȤȡ
߼ѢDBEȢDAEơ15Ǥ뤫BAP75Ȥʤ롣
äơAPB75Ȥʤ롣
ٻΤ桡 423ڡ 7:27:36 48987
ֿء׾ι
Υ٥ǤϤʤΤǤФգ£ä˿УȤҤޤ
УȡᣱȤޤУãȤդ椫顢ãȡ壳Ǥ
ޤУ£Ȥǡ£ȡᣲ+壳У¡壶ܢ売ĭǤ
äơգ£á£ȡܣȣáᣲܣ壳Ǥ顢
գ¡£á売売ܢ壶ȤʤꡢΣУ¤Ȱפޤ
äơ£С£ޤ
423ڡ 7:36:46 48988
ֿء׾ι
#48987̴

ܣģСܣģŤϤɤƤǤ
423ڡ 7:46:05 48989
Ф
ݤʤɥ󤯤餶ʤä
κä򻲹ͤˤ
BPC135٤PBP¦αĹQPQC90
ȤȢPQCPQQCľ2ջѷˤʤ롣
PQ=QC=1ȤBQcot152+3äPB1+3
ǢBPC梤AQCAQ(1+3)/2
PAQ˲­RȤAR(6)/2RP2/2
APR60äƢAPQ60+45105
٤75
423ڡ 8:52:20 MAIL:hbmath1965@yahoo.co.jp 48990
̴
#48989 ֿء׾ι

PľAEˤ뤳ȤξǤͤ͡ƤΤǤ
桹񤷤
ʲͤѤޤ߼ѤΤǡAEBADB
60äơBAE75롡APB75
ٻΤ桡 423ڡ 10:29:09 48991
󤵤󤵤󤵤󤵤
äñ
423ڡ 10:45:02 48992

CPP¦αĹˢQBC=30ȤʤQȤȢQBCջѷˤʤ
AQϤȤBCοľʬˤ
ABQȢPBQBQȤξüγѡ15120ˤΤǹƱǤAQ=PQ
APQĺѤ120ջѷǤΤѤϤ줾30
BPQϢBCPγѤǤ뤳Ȥ45
Ѥ30+45=75

ѷΤϵŤʤäɸƤߤФ褯ޤΰǤ

423ڡ 11:15:01 48993

CPP¦αĹˢQBC=30ȤʤQȤȢQBCջѷˤʤ
AQϤȤBCοľʬˤ
ABQȢPBQBQȤξüγѡ15120ˤΤǹƱǤAQ=PQ
APQĺѤ120ջѷǤΤѤϤ줾30
BPQϢBCPγѤǤ뤳Ȥ45
Ѥ30+45=75

ѷΤϵŤʤäɸƤߤФ褯ޤΰǤ

423ڡ 12:30:54 48994

ߤޤ
äɤƤޤƤޤޤ
423ڡ 12:35:46 48995
ֿء׾ι
#48991̴
꤬Ȥޤ
Ǥ⡢äѤꣳСŤľˤ뤫
äƤ褦˻פΤǤ
423ڡ 12:40:25 48996
ʤ
ѷABDȤʤDBCγ¦ˤȤȥࡼ˲򤱤ޤ͡
423ڡ 14:08:32 MAIL:junsan23@ezweb.ne.jp 48997
ʤ
ĿŪˤؤߡޤŨȻפޤ
423ڡ 14:12:35 MAIL:junsan23@ezweb.ne.jp 48998
̻
Ф魯ߤDz򤱤ޤ

ߤˡν񤭹ߤ
ʸޤ
423ڡ 14:39:29 48999
鯤ο
48978
ߤˤĤƤϡ
ߤʤС顢줬ΰĤȤϸäƤɤΤ
ȡߤˤʤʤ¾ˤʤȤ򼨤ƤʤΤ
ԴȻפޤ
ĤޤꡢͿ줿顢ɬߤǤ뤳Ȥ򼨤ɬ
ޤ

#48980
ǥץʲǤ

Dz򤱤ʤСܱߤͤФ褤櫓ǡʲξԤ路Ǥ

APCγܱߤ濴DȤȡ
BD=PD=CDǤꡢ
BDCBDP+CDP2*BCP+2*CBP2*(30+15)90
ꡢBDCľջѷȤʤꡢBACȹƱǡBA=BD
ޤPBD60ȤʤΤǡPBDѷȤʤꡢBP=BD
äơBABDBP顢BAPջѷ
äơAPB(180-30)/275
//
423ڡ 18:00:58 49000
ʥ祦󥤥
ǤPΰ֤ɬĤޤ͡
423ڡ 18:56:59 MAIL:junsan23@ezweb.ne.jp 49001
鯤ο
#49000

­ǤߤĸĤƲ򤤤ȻפäƤԽʬ㡣

ʿ̾OA=OB1ջѷOAB롣OABѤ3/4λ
ABĹ衣

OABѷˤʤߤ򸫤ĤơAB=1ȻפäƤ⡢
¤ξϡOAB߳ѻѷˤʤߤ
ꡢAB=3ʤ櫓Ǥ

ߤȤäƲ򤯾ϡʤ褦ǤäƤ⡢
Ǥ뤳Ȥ򡢲餫ˡǰźɬ
櫓Ǥ
423ڡ 20:39:08 49002
٥륯åĥ
ѷPBCBCդȤƤξüγѤͿƤΤǡPΰ֤ϳǤ
˰դͭѷηϰŪʤΤǡѤƲ򤯤Τꤵ줿ˡȤȤϤʤǤ͡
פĤޤ񤭹ߤޤ
423ڡ 21:26:48 49003

ABDC
BDդȤѷĺˤΤĺP'Ȥ
PBD=15+45=60롢P'BD=60ʤΤP'ľPˤ
DCP=30+45=75롢DCP'=75ʢDCP'ĺ30ջѷǤ뤳ȤˤʤΤP'ľCPˤ
äBPCPθǤPP'Ȱפ
äƢABPĺѤ30ջѷǤΤǵѤ75

ʤ餤ʡ
424ʶ 11:36:39 49004

#49002
ɤǤ⤤Ǥ
Ϳ줿餫˷1ĤޤΤǡߤ1ĸĤOKȻפޤ
ԡ 424ʶ 14:20:40 49005
SECOND
#49002
­ǤOA ˽ŤͤȡOB ϡޤоΤ˸١
ͭΣĤ̤ȡؤ롦ͤࡢǧˡ
425ڡ 13:59:39 49006
ϥ饮㡼ƥ
Mathematicaˤ׻Ǥ

ʤϽޤǤ
ԡ 425ڡ 17:44:51 HomePage:湩ؤ˥49007
鯤ο
#49004

̤Ǥ
˸ơߤDz򤯾ϡPPפ뤳ȤĤʤԴʤΤǤˡ㤦ΤǤ顣
425ڡ 17:47:28 49008
ߤ
ͳѷ£ãĤꡢ
¡£áã
ѣ¡ᣱ١ѣáᣴ
λѣĤ礭ϡ

¿ѷߤDzͭ̾ʻǤϤäȻפˤǤ
ˡǤϾƻǤϤʤΤǤ礦
425ڡ 18:30:12 49009
Bamboo
ߤˤʤäƤ뤳Ȥ򼨤ʤäƤȤʤ󤸤ʤΤ
ߤ󤵤μǤϽοޤ˽ѷ޳ѷ񤭲äΤǤβߤǤ뤳Ȥ뤱ɡλǤϤʤäƤʤ󤸤ʤǤ礦
ȡPȿ褿ĺ֤Ƚ뻰ѷѷǤ뤳Ȥ򼨤ѷǤΤȤƲƳΤϥǤ礦
425ڡ 23:59:41 49010
ߤ
ѷȤ߹碌褯ޤˤʤꤽ
äѤפä̤å
ĤȤΤϥ衢Ȳ򤤤Ȥǧʤ衢ȤȤǤ͡

ؤʤ餽̤ʤɡʤ餽ޤ׵ᤷʤ󤸤ʤʤʤɤǤɤƤ뤫ˤʤޤ
޷Ǻ٤Ĺ٤ʤɤξ郎ʤΤ򤤤ȤˡԹ褯
ü첽Ʋ򤯤Τ⻻ʤ饢ȻפäƤޤΤꡢ
üʾʳǤΩΤ򤭤Ⱦ٤פȤɤ
֤ȤꤢϽФ餤פȤɤιͤΰ㤤ʤΤǤ礦
426 0:47:17 49011
Ф
ʤˤʿͤ¿ΤǡʤΤϤ

ͳѷ£ãĤꡢܣᣴ롢ܣġᣵ롢¡ᣱ£áᣲ
ãġ壳ΤȤܣä礭ʤ
426 16:06:36 49012
Ȥ
#49012

ߤޤ70
ϺޤȤȤǤ
˭ԡ 426 23:16:45 MAIL:fttnm528@ybb.ne.jp 49013
Ȥ
#49012

ߤޤ70
ϺޤȤȤǤ
˭ԡ 426 23:20:43 MAIL:fttnm528@ybb.ne.jp 49014
Ȥ
#49012

ߤޤ110ǤɤƱ񤭹ߤ
˭ԡ 426 23:26:44 MAIL:fttnm528@ybb.ne.jp 49015
Ȥ
#49012

ޤȤޤ
ʤʤѤä褦ʵޤ!!

AB,DCθEȤ
AED=180-40-50=90ľѤ
ABCD=AED-BEC=BCD+ABD
ǢAED,BECľѻѷ
BE=a,EC=sqrt(4-a^2)
BEC=a*sqrt(4-a^2)/2
AED=(a+1)*(sqrt(4-a^2)+sqrt(3))/2
AED-BEC=(sqrt(4-a^2)+sqrt(3)*a+sqrt(3))/2(1)
ޤ
BCD=2*sqrt(3)*sin(BCD)/2=2*sqrt(3)*(a/2)/2=sqrt(3)*a/2
ABD=sin(2*%pi/9)*sqrt(2*sqrt(3)*sqrt(4-a^2)+2*a+8)/2
BCD+ABD=
(sqrt(2)*sin(2*%pi/9)*sqrt(sqrt(3)*sqrt(4-a^2)+a+4)+sqrt(3)*a)/2
(1)
sqrt(2)*sin(2*%pi/9)*sqrt(sqrt(3)*sqrt(4-a^2)+a+4)-sqrt(4-a^2)-sqrt(3)
ѷ
2*sqrt(3)*sin(2*%pi/9)^2*sqrt(4-a^2)-2*sqrt(3)*sqrt(4-a^2)+a^2+2*sin(2*%pi/9)^2*a+8*sin(2*%pi/9)^2-7
ѷ
a^4+4*sin(2*%pi/9)^2*a^3-(-16*sin(2*%pi/9)^4+8*sin(2*%pi/9)^2+2)*a^2
-(28*sin(2*%pi/9)**2-32*sin(2*%pi/9)^4)*a+16*sin(2*%pi/9)^4-16*sin(2*%pi/9)^2+1
aˤĤƲ򤯤
a=2*sqrt(3)*sin(2*%pi/9)*sqrt(1-sin(2*%pi/9)^2)-2*sin(2*%pi/9)^2+1
ѷ
a=2*sqrt(3)*cos(2*%pi/9)*sin(2*%pi/9)+2*cos(2*%pi/9)^2-1
sin(BCE)=a/2
sin(3*a)=3*sin(a)-4*sin(a)^3=-1/2XMaxima
factor(ev(3*sin(a)-4*sin(a)^3+1/2,sin(a)=(2*sqrt(3)*cos(2*%pi/9)*sin(2*%pi/9)+2*cos(2*%pi/9)^2-1)/2))$
trigreduce(%);0 3*sin(a)-4*sin(a)^3=-1/2BCE=70
C=BCD=180-BCE(=70)=110롦()
˭ԡ 427ʷ 0:47:20 MAIL:fttnm528@ybb.ne.jp 49016
ֿء׾ι
#49012ѴؿȤޤ
ABαĹDCαĹȤθEȤޤEľѤǤ
sinC=BE/CB
ޤã^2=£^2+ţ^2ADˤĤƤ
2^2=(Dcos40-1)^2+(ADsin40-root3)^2
AD=4sin70(ޤ)
äơBE=4sin70cos40-1=2(sin110+sin30)-1=2sin110Ѥ¤ˡ
äơsinC=BE/CB=2sin110/2=sin110

ʤǻ֤Ƥޤޤ͡
427ʷ 5:23:04 49017
Ф
ͤ͡ĺ꤬Ȥޤ
Ȥ⤵󡧥եȤΤȤϤ褯狼ޤ󡣤ߤޤ
ؾιԤ󡧻ѴؿǹԤΤˤϤäȶäޤˤʤꤽ
ϤʻϤäȿߤΤǤ뤬
ϤᤳߤäƻѴؿ˻Ȥ¿ϲ򤱤Ǥ礦͡
ʤϹͤ򤹤򤤥ҥȤ

񤭤ޤϤᤳߤήԤäƤ뤫顢ϤᤳΤѷʤ衣
1:2:3λѷäƤϤᤳȼĥĤǤλβ
#48990Ǥ⤽ĤäΤǤɤäƤߤƤʤľ23ѷ

AܢD90٤ǣ2壳Ȥͭ̾¤ǤΤ1:2:3λѷ񤭤ʤޤ
EͳѷABCDγ¦ˤȤꡢBE=1CE=3Ȥʤ褦˼ޤ
ABCDαĹθFȤޤȢCDE2ջѷ
CDEECFġ1
ƱͤˤƣEABEBFġ2ˡBCFEƱ߼ˤ뤫FCEEBFġ3
1ˡ2ˡ3ˤˤEAB=CDEäƢAEBCEDAED=90١
EAB梤EDC2Ѥˤ椬1:3AE:ED1:3
ޤȤȢAEDAE:ED1:3ǢE90٤EAD60٤Ǥ롣EABEDC20١ECD140١BCDECDݢECB140-30110

427ʷ 21:13:30 MAIL:hbmath1965@yahoo.co.jp 49018
鯤ο
#49012

ԴǤɤ

ABCDθEȤȡAEED
()AEDFD2FC=1ȤʤFȤȡ
FDC30롢FCED
ǡABFCAB//FCꡢABCFʿԻշ
顢AFBC=2FD
ꡢAFDջѷ
äơDAFADF50-3020
BCFBAF=BADݢDAF40-2020
CBCF+FCD20+90110

βԴʤȤ
()FAED¦ˤȤݾڤʤȡ

427ʷ 23:15:59 49019
SECOND
!#49012
!ؤǤʤ׻ɡ 10^-15 ʲüʤ郎С
!Ʊ٤ζͤˡ֤Ǽ«BASICǼ¹ԡ̢DCB= 110

OPTION ARITHMETIC COMPLEX
LET A=COMPLEX(0, 2)
LET B=EXP(COMPLEX(0,-40*PI/180))+A
LET D=A+5
DO
LET C=SQR(3)*EXP(COMPLEX(0, PI+50*PI/180))+D
LET BC=ABS(B-C)
LET D=D-(BC-2)
LOOP UNTIL BC=2
PRINT "DCB=";arg((B-C)/(D-C))*180/PI;""
427ʷ 23:22:07 49020
鯤ο
#49019


FAD˴ؤE¦ˤꡢAE˴ؤD¦ˤꡢED˴ؤA¦ˤ뤳Ȥ줾켨뤫顢ʤǤ
427ʷ 23:23:30 49021
٥륯åĥ
ǤСְդȤξüγˤΤǻѷPBCP'BCϹƱפΰʸʤȡƥȤȸ줽Ǥ͡
ʤ顢뤤ϿؤǤǤʤñʤ鼫ʤΤǽ񤤤ƤʤƤʤȻפޤ
429ʿ 20:49:38 49022
٥륯åĥ
ˤʤäƤޤ
429ʿ 20:50:02 49023
鯤ο
#49022

ΤˤϡPBCȢP'BCƱʤǤܤǡ
ABCȢPBCаִطȡABCȢP'BCаִطƱޤǸʤȥᡣ
ޤ߲ˡϡʣ򤬤褦ξ硢¾ˡ̤β򤬽ФʤȤݾڤʤ

顢Ҥ᤭ߤĤä顢դ˸ξDޤᤤ

429ʿ 23:29:26 49024