Matematik
Hjælp til matematik!
14. september 2012 af
Gymgy (Slettet)
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Niveau: B-niveau
Er der nogle der vil se om jeg regner rigtigt?
<p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">Figuren viser trekant <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Italic">ABC<span style="font-size:12.0pt;line-height:115%;font-family:"Century Gothic","sans-serif"; mso-bidi-font-family:Times-Roman">, hvor <span style="font-size:12.0pt; line-height:115%;font-family:Symbol;mso-bidi-font-family:Symbol">Ð<span style="font-size:12.0pt;line-height:115%;font-family:"Century Gothic","sans-serif"; mso-bidi-font-family:Symbol">B <span style="font-size:12.0pt; line-height:115%;font-family:"Century Gothic","sans-serif";mso-bidi-font-family: Symbol">= 66,3o, <span style="font-size:12.0pt;line-height: 115%;font-family:Symbol;mso-bidi-font-family:Symbol">Ð<span style="font-size:12.0pt;line-height:115%;font-family:"Century Gothic","sans-serif"; mso-bidi-font-family:Symbol">C =<span style="font-size:12.0pt; line-height:115%;font-family:"Century Gothic","sans-serif";mso-bidi-font-family: Symbol"> 77,7o og |AB| = 8,0.</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman"> </o:p> <p class="MsoListParagraphCxSpFirst" style="margin-top:0cm;margin-right:0cm; margin-bottom:0cm;margin-left:18.0pt;margin-bottom:.0001pt;mso-add-space:auto; text-indent:-18.0pt;mso-list:l0 level1 lfo1;mso-layout-grid-align:none; text-autospace:none"> <span style="font-size:12.0pt;line-height: 115%;font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">Bestem længden af siden <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Italic">AC<span style="font-size:12.0pt;line-height:115%;font-family:"Century Gothic","sans-serif"; mso-bidi-font-family:Times-Roman">.</o:p> <p class="MsoListParagraphCxSpLast" style="margin-top:0cm;margin-right:0cm; margin-bottom:0cm;margin-left:18.0pt;margin-bottom:.0001pt;mso-add-space:auto; mso-layout-grid-align:none;text-autospace:none"> <span style="font-size:12.0pt; line-height:115%;font-family:"Century Gothic","sans-serif";mso-bidi-font-family: Times-Roman"> </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">Jeg vil finde siden AC vha. sinusrelationerne, da jeg ved at trekanten er skævvinklet. </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman"> </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">a / sin(A)= c/sin(C)</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman"> </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">Jeg ved siden AB også kaldet c er 8,0 og vinkel C er 77,7o.</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">Jeg starter med at finde vinkel A ved, at trække vinkel C og B fra vinkelsummen.</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman"> </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">180o – 77,7o – 66,3o = 36o </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%;font-family:"Century Gothic","sans-serif"; mso-bidi-font-family:Times-Roman"> </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">Jeg kan nu finde siden a ved først at isolere den.</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">a/sin(36) = 8,0/sin(77,7)</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">a = 8,0 x sin(36)/sin(77,7) = 4,81</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%;font-family:"Century Gothic","sans-serif"; mso-bidi-font-family:Times-Roman"> </o:p>
Svar #2
14. september 2012 af Gymgy (Slettet)
<p class="MsoListParagraphCxSpFirst" style="margin-top:0cm;margin-right:0cm; margin-bottom:0cm;margin-left:18.0pt;margin-bottom:.0001pt;mso-add-space:auto; text-indent:-18.0pt;mso-list:l0 level1 lfo1;mso-layout-grid-align:none; text-autospace:none"> <span style="font-size:12.0pt;line-height:115%;font-family:"Century Gothic","sans-serif"; mso-fareast-font-family:"Century Gothic";mso-bidi-font-family:"Century Gothic"">a) <span style="font-size:12.0pt;line-height: 115%;font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">Bestem længden af siden <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Italic">AC<span style="font-size:12.0pt;line-height:115%;font-family:"Century Gothic","sans-serif"; mso-bidi-font-family:Times-Roman">.</o:p> <p class="MsoListParagraphCxSpLast" style="margin-top:0cm;margin-right:0cm; margin-bottom:0cm;margin-left:18.0pt;margin-bottom:.0001pt;mso-add-space:auto; mso-layout-grid-align:none;text-autospace:none"> <span style="font-size:12.0pt; line-height:115%;font-family:"Century Gothic","sans-serif";mso-bidi-font-family: Times-Roman"> </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">Jeg vil finde siden AC vha. sinusrelationerne, da jeg ved at trekanten er skævvinklet. </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman"> </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">b / sin(B)= c/sin(C)</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman"> </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">Jeg ved siden AB også kaldet c er 8,0 og vinkel C er 77,7o.</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman"> </o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">b/sin(66,3) = 8,0/sin(77,7)</o:p> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;mso-layout-grid-align: none;text-autospace:none"> <span style="font-size:12.0pt;line-height:115%; font-family:"Century Gothic","sans-serif";mso-bidi-font-family:Times-Roman">b= 8,0 x sin(66)/sin(77,7) = 7,48</o:p>
Svar #3
14. september 2012 af Andersen11 (Slettet)
Siden AC kaldes også b. Man kender to vinkler i trekanten, og dermed kender man også den tredje vinkel. Man kender en sidelængde c, så de to ukendte sidelængder kan findes ved at benytte sinusrelationerne.
b/sin(B) = c/sin(C) ,
Til sidst i #2 runder du vinkel B ned til 66,0º og får derfor et lidt forkert resultat for b .
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