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Perhatikan gambar segitiga di bawah ini! Tentukan panjang AC.

Pertanyaan

Perhatikan gambar segitiga di bawah ini!


Tentukan panjang AC.

Pembahasan Soal:

Dengan menggunakan konsep aturan sinus perbandingan sisi pada segitiga maka diperoleh panjang AC:

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 AB over denominator sin space straight C end fraction end cell row cell fraction numerator AC over denominator sin space 120 degree end fraction end cell equals cell fraction numerator 12 over denominator sin space 45 degree end fraction end cell row cell fraction numerator AC over denominator sin space 120 degree end fraction end cell equals cell fraction numerator 12 over denominator sin space 45 degree end fraction end cell row cell fraction numerator AC over denominator sin space open parentheses 180 degree minus 60 degree close parentheses end fraction end cell equals cell fraction numerator 12 over denominator sin space 45 degree end fraction end cell row cell fraction numerator AC over denominator sin space 60 degree end fraction end cell equals cell fraction numerator 12 over denominator sin space 45 degree end fraction end cell row cell fraction numerator AC over denominator begin display style fraction numerator square root of 3 over denominator 2 end fraction end style end fraction end cell equals cell fraction numerator 12 over denominator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style end fraction end cell row cell fraction numerator square root of 2 over denominator 2 end fraction cross times AC end cell equals cell fraction numerator square root of 3 over denominator 2 end fraction cross times 12 end cell row AC equals cell fraction numerator 12 square root of 3 over denominator 2 end fraction cross times fraction numerator 2 over denominator square root of 2 end fraction end cell row AC equals cell fraction numerator 12 square root of 3 over denominator square root of 2 end fraction end cell row AC 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 AC equals cell fraction numerator 12 square root of 3 over denominator 2 end fraction end cell row AC equals cell 6 square root of 3 space cm end cell end table 

Dengan demikian panjang AC adalah 6 square root of 3 space cm.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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