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Pertanyaan

Diketahui segitiga ABC dengan a plus b equals 10 space cm dan besar sudut straight A equals 30 degree. Jika besar sudut straight B equals 45 degree, maka panjang sisi b adalah ... cm.

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Gunakan konsep aturan sinus.

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 end table

Ingat kembali nilai trigonometri pada sudut istimewa 30 degree dan 45 degree.

table attributes columnalign right center left columnspacing 2px end attributes row cell sin space 30 degree end cell equals cell 1 half end cell row cell sin space 45 degree end cell equals cell 1 half square root of 2 end cell end table

Diketahui segitiga ABC dengan a plus b equals 10 space cm, besar sudut straight A equals 30 degree dan besar sudut straight B equals 45 degree, akan ditentukan panjang sisi b.

Sederhanakan a plus b equals 10 space cm untuk memperoleh nilai a.

table attributes columnalign right center left columnspacing 2px end attributes row cell a plus b end cell equals 10 row a equals cell 10 minus b end cell end table

Diperoleh a equals 10 minus b. Kemudian tentukan panjang sisi b dapat dihitung dengan aturan sinus.

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 10 minus b over denominator sin space 30 degree end fraction end cell equals cell fraction numerator b over denominator sin space 45 degree end fraction end cell row cell fraction numerator 10 minus b over denominator begin display style 1 half end style end fraction end cell equals cell fraction numerator b over denominator begin display style 1 half end style square root of 2 end fraction end cell row cell open parentheses 10 minus b close parentheses cross times 1 half square root of 2 end cell equals cell b cross times 1 half end cell row cell 5 square root of 2 minus 1 half square root of 2 b end cell equals cell 1 half b end cell row cell 5 square root of 2 end cell equals cell 1 half b plus 1 half square root of 2 b end cell row cell 1 half b plus 1 half square root of 2 b end cell equals cell 5 square root of 2 end cell row cell 1 half b open parentheses 1 plus square root of 2 close parentheses end cell equals cell 5 square root of 2 end cell row cell 1 half b end cell equals cell fraction numerator 5 square root of 2 over denominator open parentheses 1 plus square root of 2 close parentheses end fraction end cell row b equals cell fraction numerator 5 square root of 2 over denominator open parentheses 1 plus square root of 2 close parentheses end fraction cross times 2 end cell row b equals cell fraction numerator 10 square root of 2 over denominator 1 plus square root of 2 end fraction space space space open parentheses rasionalkan close parentheses end cell row b equals cell fraction numerator 10 square root of 2 over denominator 1 plus square root of 2 end fraction cross times fraction numerator 1 minus square root of 2 over denominator 1 minus square root of 2 end fraction end cell row b equals cell fraction numerator 10 square root of 2 minus 10 times 2 over denominator 1 minus 2 end fraction end cell row b equals cell fraction numerator 10 square root of 2 minus 20 over denominator negative 1 end fraction end cell row b equals cell negative 10 square root of 2 plus 20 end cell row b equals cell 20 minus 10 square root of 2 end cell end table

Diperoleh nilai b equals 20 minus 10 square root of 2.

Jadi, panjang sisi b adalah 20 minus 10 square root of 2 space cm.

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