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Diketahui segitiga  dengan besar sudut  dan besar ...

Diketahui segitiga begin mathsize 14px style PQR end style dengan besar sudut begin mathsize 14px style PQR equals 60 degree end style dan besar sudut begin mathsize 14px style PRQ equals 45 degree end style. Jika panjang begin mathsize 14px style PQ equals 12 end style cm, maka panjang sisi begin mathsize 14px style PR end style adalah ....

  1. begin mathsize 14px style 6 square root of 6 end style cm

  2. begin mathsize 14px style 4 square root of 6 end style cm

  3. begin mathsize 14px style 4 square root of 3 end style cm

  4. begin mathsize 14px style 4 square root of 2 end style cm

  5. begin mathsize 14px style 3 square root of 6 end style cm

Jawaban:

Dari soal yang diberikan dapat diketahui:

begin mathsize 14px style angle PQR equals 60 degree rightwards arrow angle straight Q equals 60 degree angle PRQ equals 45 degree rightwards arrow angle straight R equals 60 degree PQ equals 12 space cm rightwards arrow straight r equals 12 space cm PR equals straight x space cm rightwards arrow straight q equals space straight x space cm end style 

Maka:

begin mathsize 14px style fraction numerator straight p over denominator sin space straight P end fraction equals fraction numerator straight q over denominator sin space straight Q end fraction equals fraction numerator straight r over denominator sin space straight R end fraction fraction numerator straight p over denominator sin space straight P end fraction equals fraction numerator straight q over denominator sin space 60 degree end fraction equals fraction numerator 12 over denominator sin space 45 degree end fraction end style 

Sehingga:

begin mathsize 14px style fraction numerator straight q over denominator sin space 60 degree end fraction equals fraction numerator 12 over denominator sin space 45 degree end fraction space space space space fraction numerator straight q over denominator begin display style fraction numerator square root of 3 over denominator 2 end fraction end style end fraction equals fraction numerator 12 over denominator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style end fraction space straight q open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses equals open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses open parentheses 12 close parentheses straight q open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses equals 6 square root of 3 space space space space space space space space space space straight q equals fraction numerator 6 square root of 3 over denominator fraction numerator square root of 2 over denominator 2 end fraction end fraction space space space space space space space space space space straight q equals 6 square root of 3 cross times fraction numerator 2 over denominator square root of 2 end fraction space space space space space space space space space space straight q equals fraction numerator 12 square root of 3 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction space space space space space space space space space space straight q equals fraction numerator 12 square root of 6 over denominator 2 end fraction space space space space space space space space space space straight q equals 6 square root of 6 end style 

Jadi, jawaban yang benar adalah A.

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