Pertanyaan

Perhatikan gambar di samping. CD = 6 . Tentukanlah panjang AB .

Perhatikan gambar di samping.

$CD = 6$ . Tentukanlah panjang $AB$ .

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

panjang adalah .

panjang

adalah

9 over 2 minus 3 over 2 square root of 3

Pembahasan

Diketahui: Pada besar sudut dan panjang sisi . Perhatikan pula dengan besar sudut , sehingga diperoleh: Kemudian pada diperoleh: Gunakan aturan sinus pada perbandingan sisi segitiga. Pada , diperoleh: Kemudian pada dengan aturan sinus, diperoleh: Dengan demikian, panjang adalah .

Diketahui:

Pada increment ACD besar sudut straight A equals 45 degree dan panjang sisi CD equals 6 .

Perhatikan pula increment ABD dengan besar sudut straight B equals 90 degree , sehingga diperoleh:

Kemudian pada increment ACD diperoleh:

Gunakan aturan sinus pada perbandingan sisi segitiga.

Pada increment ACD , diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator CD over denominator sin space straight A end fraction end cell equals cell fraction numerator AD over denominator sin space straight C end fraction end cell row cell fraction numerator 6 over denominator sin space 45 degree end fraction end cell equals cell fraction numerator AD over denominator sin space 120 degree end fraction end cell row cell fraction numerator 6 over denominator begin display style 1 half end style square root of 2 end fraction end cell equals cell fraction numerator AD over denominator sin space open parentheses 90 degree plus 30 degree close parentheses end fraction end cell row cell 6 times fraction numerator 2 over denominator square root of 2 end fraction end cell equals cell fraction numerator AD over denominator sin space 90 degree times cos space 30 degree plus cos space 90 degree times sin space 30 degree end fraction end cell row cell fraction numerator 12 over denominator square root of 2 end fraction end cell equals cell fraction numerator AD over denominator 1 times begin display style 1 half end style square root of 3 plus 0 times begin display style 1 half end style end fraction end cell row cell fraction numerator 12 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell equals cell fraction numerator AD over denominator begin display style 1 half end style square root of 3 plus 0 end fraction end cell row cell 12 over 2 square root of 2 end cell equals cell fraction numerator AD over denominator begin display style 1 half end style square root of 3 end fraction end cell row cell 6 square root of 2 end cell equals cell AD times fraction numerator 2 over denominator square root of 3 end fraction end cell row cell 2 AD end cell equals cell 6 square root of 2 open parentheses square root of 3 close parentheses end cell row cell 2 AD end cell equals cell 6 square root of 6 end cell row AD equals cell fraction numerator 6 square root of 6 over denominator 2 end fraction end cell row AD equals cell 3 square root of 6 end cell end table$

Kemudian pada increment ABD dengan aturan sinus, diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AD over denominator sin space straight B end fraction end cell equals cell fraction numerator AB over denominator sin space straight D end fraction end cell row cell fraction numerator 3 square root of 6 over denominator sin space 90 degree end fraction end cell equals cell fraction numerator AB over denominator sin space 15 degree end fraction end cell row cell fraction numerator 3 square root of 6 over denominator 1 end fraction end cell equals cell fraction numerator AB over denominator sin space open parentheses 45 degree minus 30 degree close parentheses end fraction end cell row cell 3 square root of 6 end cell equals cell fraction numerator AB over denominator sin space 45 degree times cos space 30 degree minus cos space 45 degree times sin space 30 degree end fraction end cell row cell 3 square root of 6 end cell equals cell fraction numerator AB over denominator begin display style 1 half end style square root of 2 times begin display style 1 half end style square root of 3 minus begin display style 1 half end style square root of 2 times begin display style 1 half end style end fraction end cell row cell 3 square root of 6 end cell equals cell fraction numerator AB over denominator begin display style 1 fourth end style square root of 6 minus begin display style 1 fourth end style square root of 2 end fraction end cell row AB equals cell 3 square root of 6 open parentheses 1 fourth square root of 6 minus 1 fourth square root of 2 close parentheses end cell row AB equals cell 3 over 4 times 6 minus 3 over 4 square root of 12 end cell row AB equals cell 18 over 4 minus 3 over 4 square root of 12 end cell row AB equals cell 9 over 2 minus 3 over 4 square root of 4 times 3 end root end cell row AB equals cell 9 over 2 minus 3 over 4 times 2 square root of 3 end cell row AB equals cell 9 over 2 minus 6 over 4 square root of 3 end cell row AB equals cell 9 over 2 minus 3 over 2 square root of 3 end cell end table$

Dengan demikian, panjang adalah 9 over 2 minus 3 over 2 square root of 3 .