Pertanyaan

Diketahui segitiga ABC dengan panjang AC = 12 cm , ∠ BAC = 45° dan ∠ ABC = 6 0 ∘ ,hitunglah panjang BC!

Diketahui segitiga ABC dengan panjang $AC = 12 cm$ , $∠ BAC$ = 45° dan $∠ ABC = 6 0^{\circ}$ , hitunglah panjang BC!

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Habis dalam

Klaim

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Pembahasan

Perhatikan gambar berikut. Berdasarkan aturan sinus, maka Jadi, panjang BC adalah .

Perhatikan gambar berikut.

Berdasarkan aturan sinus, maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator sin space straight A end fraction end cell equals cell fraction numerator b over denominator sin space straight B end fraction end cell row cell fraction numerator BC over denominator sin space straight A end fraction end cell equals cell fraction numerator AC over denominator sin space straight B end fraction end cell row cell fraction numerator BC over denominator sin space 45 degree end fraction end cell equals cell fraction numerator 12 over denominator sin space 60 degree end fraction end cell row cell fraction numerator BC over denominator begin display style 1 half end style square root of 2 end fraction end cell equals cell fraction numerator 12 over denominator begin display style 1 half end style square root of 3 end fraction end cell row BC equals cell fraction numerator 12 cross times 1 half square root of 2 over denominator 1 half square root of 3 end fraction end cell row BC equals cell fraction numerator 12 square root of 2 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row BC equals cell fraction numerator 12 square root of 6 over denominator 3 end fraction end cell row BC equals cell 4 square root of 6 space cm end cell end table$

Jadi, panjang BC adalah 4 square root of 6 space cm .