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Diketahui segitiga PQR dengan panjang sisi  dan . ...

Diketahui segitiga PQR dengan panjang sisi begin mathsize 14px style p comma space q comma space r end style dan begin mathsize 14px style q cross times r equals 12 square root of 3 space cm end style. Jika besar sudut Q adalah begin mathsize 14px style 120 degree end style dan sudut R adalah size 14px 30 size 14px degree, panjang sisi PQ adalah ....

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

  2. begin mathsize 14px style 2 square root of 3 space cm end style 

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

  4. begin mathsize 14px style 3 square root of 2 space cm end style 

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

Jawaban:

Masalah yang diberikan di atas dapat diilustrasikan sebagai berikut.

Diketahui:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell q cross times r end cell equals cell 12 square root of 3 end cell row blank rightwards double arrow cell q equals fraction numerator 12 square root of 3 over denominator r end fraction end cell row cell angle straight Q end cell equals cell 120 degree end cell row cell angle straight R end cell equals cell 30 degree end cell end table end style 

Sehingga dapat ditentukan panjang PQ sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator PQ over denominator sin space angle straight R end fraction end cell equals cell fraction numerator PR over denominator sin space angle straight Q end fraction end cell row cell fraction numerator r over denominator sin space 30 degree end fraction end cell equals cell fraction numerator q over denominator sin space 120 degree end fraction end cell row r equals cell fraction numerator q over denominator sin space 120 degree end fraction cross times sin space 30 degree end cell row blank equals cell fraction numerator q over denominator up diagonal strike begin display style 1 half end style end strike square root of 3 end fraction cross times up diagonal strike 1 half end strike end cell row blank equals cell fraction numerator q over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 12 up diagonal strike square root of 3 end strike over denominator r end fraction end style over denominator up diagonal strike square root of 3 end strike end fraction end cell row blank equals cell 12 over r end cell row cell r squared end cell equals 12 row r equals cell plus-or-minus square root of 12 end cell row blank equals cell plus-or-minus 2 square root of 3 end cell row blank equals cell 2 square root of 3 space left parenthesis panjang space selalu space positif right parenthesis end cell end table end style 

Dengan demikian, panjang PQ adalah begin mathsize 14px style 2 square root of 3 space cm end style.

Jadi, jawaban yang benar adalah B.

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