Pertanyaan

Diketahui segitiga ABC , dengan BC = 6 , AC = 8 , dan ∠ A = 3 0 ∘ . Nilai cos ∠ B adalah ....

Diketahui segitiga $ABC$ , dengan $BC = 6, AC = 8$ , dan $∠ A = 3 0^{\circ}$ . Nilai $cos ∠ B$ adalah ....

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai adalah .

nilai

adalah

Pembahasan

Diketahui: Maka: Sehingga: Diperoleh: Jadi, nilai adalah .

Diketahui:

BC equals 6 space rightwards arrow space straight a equals 6 AC equals 8 space rightwards arrow space straight b equals 8 angle straight A equals 30 degree

Maka:

$space space space space space fraction numerator straight a over denominator sin space straight A end fraction equals fraction numerator straight b over denominator sin space straight B end fraction space fraction numerator 6 over denominator sin space 30 degree end fraction equals fraction numerator 8 over denominator sin space straight B end fraction space space space space space space space space fraction numerator 6 over denominator begin display style 1 half end style end fraction equals fraction numerator 8 over denominator sin space straight B end fraction 6 cross times sin space straight B equals 8 cross times 1 half 6 cross times sin space straight B equals 4 space space space space space space sin space straight B equals 4 over 6 space space space space space space sin space straight B equals 2 over 3 rightwards arrow sin space straight B equals fraction numerator sisi space depan over denominator sisi space miring end fraction$

Sehingga:

sisi space samping equals square root of 3 squared minus 2 squared end root sisi space samping equals square root of 9 minus 4 end root sisi space samping equals square root of 5

Diperoleh:

$cos space straight B equals fraction numerator sisi space samping over denominator sisi space miring end fraction cos space straight B equals fraction numerator square root of 5 over denominator 3 end fraction cos space straight B equals 1 third square root of 5$

Jadi, nilai cos space angle straight B adalah 1 third square root of 5 .