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SMK Teknologi dan Rekayasa

Soal 88 Perbandingan Trigonometri


Pada\ gambar\ segitiga\ ABC\ berikut\ ini\ panjang\ AC\ adalah\ ....

a.\ \ 2\sqrt{6}\ \ \ \ \ \ \ \ \ \ b.\ \ 4\sqrt{6}\ \ \ \ \ \ \ \ \ \ c.\ \ 8\sqrt{6}\ \ \ \ \ \ \ \ \ \ d.\ \ 2\sqrt{2}\ \ \ \ \ \ \ \ \ \ e.\ \ 4\sqrt{2}
Jawaban: e

Karena\ jumlah\ besar\ sudut\ pada\ segitiga\ adalah\ 180^{\circ},\ maka\ \angle B=45^{\circ}
Aturan\ Sinus:\ \ \ \ \ \ \ \ \frac{AC}{sin\ B}=\frac{BC}{sin\ A}
\begin{array}{rcl}AC&=&\frac{BC}{sin\ A}\ \times \ sin\ B\\\\&=&\frac{4\sqrt{3}}{sin\ 60^{\circ}}\ \times \ sin\ 45^{\circ}\\\\&=&\frac{4\sqrt{3}}{\frac{1}{2}\sqrt{3}}\ \times \ \frac{1}{2}\sqrt{2}\\\\&=&4\sqrt{2}\end{array}

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