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#28308, #28310
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¢¤PAD ¢æ ¢¤ADC ¤«¤é¡¢CD¡§AD = AC¡§PA = 8¡§5 ¤Ç¡¢CD = AD * 8/5 = = 8 * 8/5 = 64/5 cm¡¢BC = BD + CD = 8 + 64/5 = 104/5 cm ¤Ê¤Î¤Ç¡¢
¢¤ABC = 1/2 * BC * AH = 1/2 * 104/5 * 24/5 = 1248/25 = 49.92 cm^2 ¤Ç¤¹¤Í¡£

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AB ¤Ë´Ø¤·¤Æ ¢¤ABP ¤òÀÞ¤êÊÖ¤¹¤Î¤Ï»ä¤Î#28327¤Î(²òË¡2)¤ÈƱ¤¸¤Ç¤¹¤¬¡¢¤Ê¤ë¤Û¤É¡¢¤½¤Î¸å¤¬¤¦¤Þ¤¤¤Ç¤¹¤Í¡£
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>e1:13*d^2-c^2*d+194*d-507=0$
>e2:5*c^2*d^2-8*c^4+2259*c^2-165888=0$
>solve([e1,e2],[c,d]);
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d=sqrt(16849)/26-25/26
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¢ÜABC = x, ¢ÜACB = y ¤È¤·¤Þ¤¹¡£¤¹¤ë¤È¡¢¢ÜBAP = x+y, ¢ÜAPC = 2x+y, ¢ÜAPB = 180-(2x+y) ¤Ç¤¹¡£
¤½¤·¤Æ¡¢µá¤á¤ë ¢¤ABP ¤ÎÌÌÀѤϡ¢
¢¤ABP = 1/2 * BP * AP * sin(¢ÜAPB) = 1/2 * BP * AP * sin(2x+y)
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¢¤ABP ¤ËÀµ¸¹ÄêÍý¤ò»È¤Ã¤Æ¡¢sin(¢ÜABP)/AP = sin(¢ÜBAP)/BP¡¢¤Ä¤Þ¤ê¡¢sin(x)/5 = sin(x+y)/13
¢¤ACP ¤ËÀµ¸¹ÄêÍý¤ò»È¤Ã¤Æ¡¢sin(¢ÜACP)/AP = sin(¢ÜAPC)/AC¡¢¤Ä¤Þ¤ê¡¢sin(y)/5 = sin(2x+y)/8
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13/5 = sin(x+y)/sin(x)
8/5 = sin(2x+y)/sin(y)
1 = 13/5 - 8/5 = sin(x+y)/sin(x) - sin(2x+y)/sin(y)
ʬÊì¤òʧ¤Ã¤Æ
sin(x) * sin(y) = sin(x+y) * sin(y) - sin(2x+y) * sin(x)
ÀѤòϤËÊÑ·Á¤·¤Æ
cos(x+y) - cos(x-y) = cos(x+2y) - cos(x) - cos(3x+y) + cos(x+y)
- cos(x-y) = cos(x+2y) - cos(x) - cos(3x+y)
cos(3x+y) - cos(x-y) = cos(x+2y) - cos(x)
ϤòÀѤËÊÑ·Á¤·¤Æ
six(2x) * sin(x+y) = sin(x+y) * sin(y)
0 < x+y < 180 ¤Ê¤Î¤Ç sin(x+y) ¡â 0 ¤Ç¡¢
sin(2x) = sin(y)
0 < 2x, y, 2x+y < 180 ¤Ê¤Î¤Ç¡¢
2x = y
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sin(2x+y)/sin(y) = 8/5
sin(2y)/sin(y) = 8/5
ÇܳѤθø¼°¤è¤ê
2 * sin(y) * cos(y) / sin(y) = 8/5
cos(y) = 4/5
sin(y) = 3/5
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sin(2x+y) = 3/5 * 8/5 = 24/25
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¢¤ABP = 1/2 * BP * AP * sin(2x+y) = 1/2 * 13 * 5 * 24/25 = 13 * 12/5 = 156/5 cm^2
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¡ä>e1:13*d^2-c^2*d+194*d-507=0$
¡ä>e2:5*c^2*d^2-8*c^4+2259*c^2-165888=0$
¡ä>solve([e1,e2],[c,d]);
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¡äc=sqrt(2)*sqrt(2579/2-5*sqrt(16849)/2)/4
¡äd=sqrt(16849)/26-25/26
¡ä¤ÇÅú¤¨¤¬
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(¶õÇò¤¬¤¦¤Þ¤¯É½¼¨¤µ¤ì¤ë¤«¿´ÇۤǤ¹¤¬¡¥¡¥¡¥)

OPTION ANGLE DEGREES
LET c = 24/5 * SQR(10)
LET d = 39/5
LET a = ACOS((c^2 + 13^2 - 5^2)/(2 * 13 * c))
LET b = ACOS((d^2 + 8^2 - 5^2)/(2 * 8 * d))
LET f = ACOS((c^2 + 5^2 - 13^2)/(2 * 5 * c))
PRINT "º£²ó¤ÎÌäÂê¤Î¾ì¹ç"
PRINT "¢ÜABP ¡¡¡¡¡¡¡¡="; a
PRINT "¢ÜACP ¡¡¡¡¡¡¡¡="; b
PRINT "¢ÜABP + ¢ÜACP ="; a+b
PRINT "¢ÜBAP ¡¡¡¡¡¡¡¡="; f
PRINT
LET c = SQR(2579 - 5 * SQR(16849))/4
LET d = (SQR(16849) - 25)/26
LET a = ACOS((c^2 + 13^2 - 5^2)/(2 * 13 * c))
LET b = ACOS((d^2 + 8^2 - 5^2)/(2 * 8 * d))
LET f = ACOS((c^2 + 5^2 - 13^2)/(2 * 5 * c))
PRINT "¥´¥ó¤È¤â¤µ¤ó¤Î¤â¤¦°ì¤Ä¤Î¾ì¹ç¡©"
PRINT "¢ÜABP ¡¡¡¡¡¡¡¡="; a
PRINT "¢ÜACP ¡¡¡¡¡¡¡¡="; b
PRINT "¢ÜABP + ¢ÜACP ="; a+b
PRINT "¢ÜBAP ¡¡¡¡¡¡¡¡="; f
END

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¢ÜABP ¡¡¡¡¡¡¡¡= 18.4349488229221
¢ÜACP ¡¡¡¡¡¡¡¡= 36.869897645844
¢ÜABP + ¢ÜACP = 55.3048464687661
¢ÜBAP ¡¡¡¡¡¡¡¡= 55.3048464687663

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¢ÜABP ¡¡¡¡¡¡¡¡= 22.0739261091459
¢ÜACP ¡¡¡¡¡¡¡¡= 31.0592862475447
¢ÜABP + ¢ÜACP = 53.1332123566906
¢ÜBAP ¡¡¡¡¡¡¡¡= 102.288929214437

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