Pertanyaan

Pada segitiga ABC , jika AB = 1 , AC = 12 , sin B = 5 4 . Maka carilah nilai cos C .

Pada segitiga $ABC$ , jika $AB = 1$ , $AC = 12$ , $sin B = \frac{4}{5}$ . Maka carilah nilai $cos C$ .

N. Sari

Master Teacher

Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Pembahasan

Dengan menggunakan aturan sinus, maka didapatkan perbandingan : Dari nilai sinus diketahui : Sehingga sisi sampingnya : Maka, cosinusnya : Maka,

Dengan menggunakan aturan sinus, maka didapatkan perbandingan :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AC over denominator sin space B end fraction end cell equals cell fraction numerator AB over denominator sin space C end fraction end cell row cell fraction numerator 12 over denominator 4 over 5 end fraction end cell equals cell fraction numerator 1 over denominator sin space C end fraction end cell row cell sin space C end cell equals cell 4 over 5 cross times 1 over 12 end cell row cell sin space C end cell equals cell 1 over 15 end cell end table$

Dari nilai sinus diketahui :

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space C end cell equals cell 1 over 15 end cell row cell depan over miring end cell equals cell 1 over 15 end cell end table

Sehingga sisi sampingnya :

table attributes columnalign right center left columnspacing 0px end attributes row samping equals cell square root of 15 squared minus 1 squared end root end cell row blank equals cell square root of 225 minus 1 end root end cell row blank equals cell square root of 224 end cell row blank equals cell 4 square root of 14 end cell end table

Maka, cosinusnya :

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space C end cell equals cell samping over miring end cell row blank equals cell fraction numerator 4 square root of 14 over denominator 15 end fraction end cell end table$

Maka, $table attributes columnalign right center left columnspacing 0px end attributes row cell cos space C end cell equals cell fraction numerator 4 square root of 14 over denominator 15 end fraction end cell end table$