Pertanyaan

Diketahui △ ABC , panjang sisi AC = 8 cm , ∠ A = 6 0 ∘ , ∠ B = 7 5 ∘ .Tentukan panjang sisi BC dan sisi AB!

Diketahui $△ ABC$ , panjang sisi $AC = 8 cm$ , $∠ A = 6 0^{\circ}$ , $∠ B = 7 5^{\circ}$ . Tentukan panjang sisi BC dan sisi AB!

R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

dan .

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

Pembahasan

Perhatikan gambar berikut! Nilai sinus sudut B adalah Dengan aturan sinus diperoleh panjang sisi BC, yaitu Jumlah sudut dalam segitiga adalah , sehingga . Dengan aturan sinus diperoleh panjang sisi AB sebagai berikut, Jadi, dan .

Perhatikan gambar triangle ABC berikut!

Nilai sinus sudut B adalah

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 .

Latihan Bab

Konsep Kilat

Derajat dan Radian

Perbandingan Sisi (Trigonometri)

Sudut Istimewa (Trigonometri)