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Panjang BC dari segitiga berikut....

Pertanyaan

Panjang BC dari segitiga berikut...cm.

Pembahasan Soal:

Dengan menggunakan aturan sinus diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator BC over denominator sin open parentheses straight A close parentheses end fraction end cell equals cell fraction numerator AC over denominator sin open parentheses straight B close parentheses end fraction end cell row cell fraction numerator BC over denominator sin open parentheses 60 degree close parentheses end fraction end cell equals cell fraction numerator 12 over denominator sin open parentheses 45 degree close parentheses end fraction end cell row cell fraction numerator BC over denominator begin display style 1 half end style square root of 3 end fraction end cell equals cell fraction numerator 12 over denominator begin display style 1 half end style square root of 2 end fraction end cell row BC equals cell fraction numerator 12 cross times begin display style 1 half end style square root of 3 over denominator begin display style 1 half end style square root of 2 end fraction end cell row blank equals cell fraction numerator 12 square root of 3 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 12 square root of 6 over denominator 2 end fraction end cell row blank equals cell 6 square root of 6 space cm end cell end table

Dengan demikian panjang BC adalah 6 square root of 6 space cm.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Nur

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Terakhir diupdate 02 Mei 2021

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Pertanyaan yang serupa

Jika diketahui segitiga ABC, dengan ukuran panjang sisi  dan panjang sisi  dan . Hitung besar ,  dan panjang !

Pembahasan Soal:

1

Roboguru

Diberikan segiempat ABCD seperti pada gambar! Panjang BC adalah...

Pembahasan Soal:

Menentukan panjang AC menggunakan aturan sinus

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AC over denominator sin space straight D end fraction end cell equals cell fraction numerator AD over denominator sin space straight C end fraction end cell row cell fraction numerator AC over denominator sin space 30 degree end fraction end cell equals cell fraction numerator 10 over denominator sin space 45 degree end fraction end cell row cell fraction numerator AC over denominator begin display style 1 half end style end fraction end cell equals cell fraction numerator 10 over denominator begin display style 1 half end style square root of 2 end fraction end cell row cell AC cross times 1 half square root of 2 end cell equals cell 1 half cross times 10 end cell row AC equals cell fraction numerator 1 half cross times 10 over denominator 1 half square root of 2 end fraction end cell row AC equals cell fraction numerator 10 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row AC equals cell fraction numerator 10 square root of 2 over denominator 2 end fraction end cell row AC equals cell 5 square root of 2 space cm end cell end table 

Menentukan panjang BC menggunakan aturan cosinus

table attributes columnalign right center left columnspacing 0px end attributes row BC equals cell square root of AB squared plus AC squared minus 2 times AB times AC times cos space straight A end root end cell row blank equals cell square root of left parenthesis 10 square root of 2 right parenthesis squared plus left parenthesis 5 square root of 2 right parenthesis squared minus 2 times 10 square root of 2 times 5 square root of 2 times cos space 60 degree end root end cell row blank equals cell square root of 200 plus 50 minus 200 times 1 half end root end cell row blank equals cell square root of 250 minus 100 end root end cell row blank equals cell square root of 150 end cell row blank equals cell square root of 25 cross times 6 end root end cell row blank equals cell 5 square root of 6 space cm end cell end table 

Jadi, jawaban yang benar adalah D.

 

2

Roboguru

Panjang sisi  pada gambar berikut adalah ....

Pembahasan Soal:

Gunakan konsep aturan sinus.

fraction numerator a over denominator sin space straight A end fraction equals fraction numerator b over denominator sin space straight B end fraction

Akan ditentukan panjang sisi b pada gambar.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator a over denominator sin space straight A end fraction end cell equals cell fraction numerator b over denominator sin space straight B end fraction end cell row cell fraction numerator BC over denominator sin space 45 degree end fraction end cell equals cell fraction numerator b over denominator sin space 30 end fraction end cell row cell fraction numerator 16 over denominator begin display style 1 half end style square root of 2 end fraction end cell equals cell fraction numerator b over denominator begin display style 1 half end style end fraction end cell row cell 16 cross times 1 half end cell equals cell b cross times 1 half square root of 2 end cell row 8 equals cell fraction numerator square root of 2 over denominator 2 end fraction b end cell row b equals cell 8 space colon space fraction numerator square root of 2 over denominator 2 end fraction end cell row b equals cell 8 cross times fraction numerator 2 over denominator square root of 2 end fraction end cell row b equals cell fraction numerator 16 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row b equals cell fraction numerator 16 square root of 2 over denominator 2 end fraction end cell row b equals cell 8 square root of 2 end cell end table

Jadi, diperoleh panjang sisi b adalah 8 square root of 2.

0

Roboguru

Perhatikan gambar berikut. Gambar di atas adalah  dengan M adalah titik pada sisi AC sedemikian sehingga . Besar , panjang sisi   a. Buktikan bahwa

Pembahasan Soal:

0

Roboguru

Diketahui , panjang sisi , , . Tentukan panjang sisi BC dan sisi AB!

Pembahasan Soal:

Perhatikan gambar triangle ABC berikut!

Nilai sinus sudut B adalah

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 75 degree end cell equals cell sin space open parentheses 45 degree plus 30 degree close parentheses end cell row blank equals cell sin space 45 degree times cos space 30 degree plus cos space 45 degree times sin space 30 degree end cell row blank equals cell 1 half square root of 2 times 1 half square root of 3 plus 1 half square root of 2 times 1 half end cell row blank equals cell 1 fourth square root of 2 open parentheses square root of 3 plus 1 close parentheses end cell end table

Dengan aturan sinus diperoleh panjang sisi BC, yaitu

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AC over denominator sin space straight B end fraction end cell equals cell fraction numerator BC over denominator sin space straight A end fraction end cell row cell fraction numerator 8 over denominator sin space 75 degree end fraction end cell equals cell fraction numerator BC over denominator sin space 60 degree end fraction end cell row cell fraction numerator 8 over denominator begin display style 1 fourth end style square root of 2 open parentheses square root of 3 plus 1 close parentheses end fraction end cell equals cell fraction numerator BC over denominator 1 half square root of 3 end fraction end cell row cell 1 fourth square root of 2 open parentheses square root of 3 plus 1 close parentheses times BC end cell equals cell 8 times 1 half square root of 3 end cell row cell 1 fourth square root of 2 open parentheses square root of 3 plus 1 close parentheses times BC end cell equals cell 4 square root of 3 end cell row cell square root of 2 open parentheses square root of 3 plus 1 close parentheses times BC end cell equals cell 16 square root of 3 end cell row BC equals cell fraction numerator 16 square root of 3 over denominator square root of 2 open parentheses square root of 3 plus 1 close parentheses end fraction end cell row BC equals cell fraction numerator 16 square root of 3 over denominator square root of 2 open parentheses square root of 3 plus 1 close parentheses end fraction times fraction numerator square root of 2 open parentheses square root of 3 minus 1 close parentheses over denominator square root of 2 open parentheses square root of 3 minus 1 close parentheses end fraction end cell row BC equals cell fraction numerator 16 square root of 6 open parentheses square root of 3 minus 1 close parentheses over denominator 2 open parentheses 3 minus 1 close parentheses end fraction end cell row BC equals cell fraction numerator 16 open parentheses square root of 18 minus square root of 6 close parentheses over denominator 4 end fraction end cell row BC equals cell 4 open parentheses 3 square root of 2 minus square root of 6 close parentheses space cm end cell end table

Jumlah sudut dalam segitiga adalah 180 degree, sehingga angle straight C equals 45 degree. Dengan aturan sinus diperoleh panjang sisi AB sebagai berikut,

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AB over denominator sin space straight C end fraction end cell equals cell fraction numerator AC over denominator sin space straight B end fraction end cell row cell fraction numerator AB over denominator sin space 45 degree end fraction end cell equals cell fraction numerator 8 over denominator sin space 75 degree end fraction end cell row cell fraction numerator AB over denominator begin display style 1 half end style square root of 2 end fraction end cell equals cell fraction numerator 8 over denominator begin display style 1 fourth end style square root of 2 open parentheses square root of 3 plus 1 close parentheses end fraction end cell row cell 1 fourth square root of 2 open parentheses square root of 3 plus 1 close parentheses times AB end cell equals cell 1 half square root of 2 times 8 end cell row cell 1 fourth square root of 2 open parentheses square root of 3 plus 1 close parentheses times AB end cell equals cell 4 square root of 2 end cell row AB equals cell fraction numerator 4 square root of 2 over denominator 1 fourth square root of 2 open parentheses square root of 3 plus 1 close parentheses end fraction end cell row AB equals cell fraction numerator 16 over denominator square root of 3 plus 1 end fraction times fraction numerator square root of 3 minus 1 over denominator square root of 3 minus 1 end fraction end cell row AB equals cell fraction numerator 16 open parentheses square root of 3 minus 1 close parentheses over denominator 3 minus 1 end fraction end cell row AB equals cell 8 open parentheses square root of 3 minus 1 close parentheses space cm end cell end table 

Jadi, BC equals 4 open parentheses 3 square root of 2 minus square root of 6 close parentheses space cm dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank AB end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses square root of 3 minus 1 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cm end table.

0

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