Pertanyaan

Diketahui segitiga PQR dengan panjang sisi PQ=p, sisi PQ=r, dan p+r=18. Jika ∠ Q = 3 0 ∘ dan ∠ p = 6 0 ∘ , maka panjang sisi PR adalah....

Diketahui segitiga PQR dengan panjang sisi PQ=p, sisi PQ=r, dan p+r=18. Jika $∠ Q = 3 0^{\circ}$ dan $∠ p = 6 0^{\circ}$ , maka panjang sisi PR adalah....

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H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

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Pembahasan

$asterisk times cos space 30 degree equals QR over PQ fraction numerator square root of 3 over denominator 2 end fraction equals straight p over straight r 2 straight p equals square root of 3 straight r left right double arrow straight p equals fraction numerator square root of 3 over denominator 2 end fraction straight r asterisk times straight p plus space straight r space equals space 18 fraction numerator square root of 3 over denominator 2 end fraction straight r plus straight r equals 18 open parentheses fraction numerator square root of 3 plus 2 over denominator 2 end fraction close parentheses straight r equals 18 straight r equals 18 space. space fraction numerator 2 over denominator 2 plus square root of 3 end fraction equals fraction numerator 36 over denominator 2 plus square root of 3 end fraction asterisk times sin space 30 degree equals PR over PQ 1 half equals PR over straight r 2 PR equals straight r 2 PR equals fraction numerator 36 over denominator 2 plus square root of 3 end fraction PR equals fraction numerator 36 over denominator 2 plus square root of 3 end fraction. space 1 half PR equals fraction numerator 18 over denominator 2 plus square root of 3 end fraction. space fraction numerator 2 minus square root of 3 over denominator 2 minus square root of 3 end fraction equals fraction numerator 36 minus 18 square root of 3 over denominator 4 minus 3 end fraction equals 36 minus 18 square root of 3$