Page 264 - Demo

258 P%u00ebrgjigjet*12 a Syprina e katrorit t%u00eb madh = (a + b)2 = c2 + 4 %u00d7 12 ab = (syprina e katrorit t%u00eb vog%u00ebl + 4 trek%u00ebnd%u00ebsha) a2 + 2ab + b2 = c2 + 2ab a2 + b2 = c2 b i Syprina e gjysm%u00ebrrethit = = 12 Sr2= . P%u00ebrdorim a dhe b p%u00ebr diametrat e gjysm%u00ebrrath%u00ebve t%u00eb vegj%u00ebl dhe c p%u00ebr rrethin e madh. Shuma e syprinave t%u00eb gjysm%u00ebrrath%u00ebve t%u00eb vegj%u00ebl = 18 Sa2 + 18 Sb2 = 18 %u03c0(a2 +b2) = 18 Sc2(Teorema e Pitagor%u00ebs) = syprin%u00ebn e gjysm%u00ebrrethit m%u00eb t%u00eb madh. ii Syprina e trek%u00ebnd%u00ebshit barabrinj%u00ebs, S = 12 bhku h2 = Syprina e trek%u00ebnd%u00ebshit barabrinj%u00ebs, Shuma e syprinave t%u00eb dy trek%u00ebnd%u00ebshave barabrinj%u00ebs, me brinj%u00eb p%u00ebrkat%u00ebsisht n%u00eb katetet e nj%u00eb trek%u00ebnd%u00ebshi k%u00ebnddrejt%u00eb = syprin%u00ebn e trek%u00ebnd%u00ebshit barabrinj%u00ebs, me brinj%u00eb hipotenuz%u00ebn e trek%u00ebnd%u00ebshit k%u00ebnddrejt%u00eb (Teorema e Pitagor%u00ebs).*13 40 2 mm 14 a Ka shum%u00eb. Disa shembuj jepen m%u00eb posht%u00eb: 3, 4, 5 5, 12, 13 7, 24, 25 b Po, duke shum%u00ebzuar t%u00eb dyja brinj%u00ebt e nj%u00eb trek%u00ebnd%u00ebshi k%u00ebnddrejt%u00eb me t%u00eb nj%u00ebjtin num%u00ebr, marrim nj%u00eb trek%u00ebnd%u00ebsh k%u00ebnddrejt%u00eb t%u00eb ngjash%u00ebm. c (2xy)2 = 4x2y2(x2 + y2)2 = x4 + 2x2y2 + y4(x2 %u2212 y2)2 = x4 %u2212 2x2y2 + y4(2xy)2 + (x2 %u2212 y2)2 = 4x2y2 + x4 %u2212 2x2y2 + y4 = (x2 + y2)27.2A1 a a = 7,5 cm b b = 29 cm, sepse tg41%u00b0 = 25b e e = 54 mm h h = 3,8 cm i i = 7,1 m2 a a = 66,4%u00b0 c c = 56,3%u00b0 f f = 29,4%u00b03 a A = 37%u00b0 C = 53%u00b0 AC = 10 cm d KL = 15 mm JK = 23 mm K = 50%u00b04 a BC = 31,5 mm b %u0486PRQ = %u0486RPQ = 73%u00b0%u0486PQR = 33%u00b05 KN = KL = 19 cm (cm m%u00eb i af%u00ebrt)NM = LM = 30 cm (cm m%u00eb i af%u00ebrt)LKN = 77%u00b0 (grada m%u00eb e af%u00ebrt)LMN = 48%u00b0 (grada m%u00eb e af%u00ebrt)KNM = KLM = 117%u00b0 (grada m%u00eb e af%u00ebrt)6 a %u0486DCB =%u0486DAB = 116%u00b0%u0486ABC =%u0486ADC = 64%u00b0 b AC = 10,5 cm*7 a b c K%u00ebndi Sin Cos Tg0%u00b0 0 1 030%u00b0 123213 = 3345%u00b0 12 = 2212 = 22160%u00b0 3212390%u00b0 1 0 %u00928 a h = 4,8 m b d = 1,3 m7.2Z1 a 36,4 m b %u00cbsht%u00eb e v%u00ebshtir%u00eb q%u00eb t%u00eb vler%u00ebsoni larges%u00ebn dhe k%u00ebndin me sakt%u00ebsi. Largesa horizontale mund t%u00eb jet%u00eb e pasakt%u00eb, p%u00ebr shkak t%u00eb nd%u00ebrtesave q%u00eb rrethojn%u00eb baz%u00ebn e kull%u00ebs. Toka mund t%u00eb mos jet%u00eb horizontale (lart%u00ebsia e v%u00ebrtet%u00eb %u00ebsht%u00eb 35 m).2 Po, lart%u00ebsia = 9,534... + 1,6 = 11,134... m > 10 m3 38 m4 9,0 m5 Syprina = 144 3 cm26 12 2 m27 81 3 mm28 Jo, tg %u03b8 = 36240 = 0,15 %u009f %u03b8 = 8,53...%u00b0 > 4%u00b09 a tgD = 2 b tgD = 3 c tgD = 12 d tgD = koeficienti k%u00ebndor i drejt%u00ebz%u00ebs = pjerr%u00ebsia e saj10 60%u00b011 a %u03b8 = 31%u00b0b Le t%u00eb jet%u00eb x lart%u00ebsia vertikale e %u00e7atis%u00eb. x2 = 142 %u2212 122 = 52, x = 52 = 2 13 Syprina e p%u00ebrgjithshme = 24 %u00d7 21 + 12 %u00d7 24 %u00d7 2 13 = 24(21 + 13) m212 Perimetri = 120 mm Syprina = 432 3 mm2*13 90%u00ba %u2013 %u03b1%u03b1HAO