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RS = ?

RS?

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Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

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Jawaban

panjang RS adalah cm.

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

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Pembahasan

Perhatikan PQR, dengan aturan cosinus: Perhatikan PRS, dengan aturan sinus: Jadi, panjang RS adalah cm.

Perhatikan begin mathsize 14px style triangle end stylePQR, dengan aturan cosinus:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell text PR end text squared end cell equals cell text PQ end text squared plus text QR end text squared minus 2 times text PQ end text times text QR end text times cos space 120 degree end cell row cell text PR end text squared end cell equals cell 4 squared plus 4 squared minus 2 times 4 times 4 times open parentheses negative 1 half close parentheses end cell row cell text PR end text squared end cell equals cell 16 plus 16 plus 16 end cell row cell text PR end text squared end cell equals 48 row cell text PR end text end cell equals cell 4 square root of 3 end cell end table end style

Perhatikan begin mathsize 14px style triangle end stylePRS, dengan aturan sinus:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator text RS end text over denominator sin space 45 degree end fraction end cell equals cell fraction numerator text PR end text over denominator sin space 60 degree end fraction end cell row cell text RS end text times sin space 60 degree end cell equals cell text PR end text times sin space 45 degree end cell row cell text RS end text times fraction numerator square root of 3 over denominator 2 end fraction end cell equals cell 4 square root of 3 times fraction numerator square root of 2 over denominator 2 end fraction end cell row cell text RS end text end cell equals cell fraction numerator 4 square root of 3 times square root of 2 over denominator square root of 3 end fraction end cell row cell text RS end text end cell equals cell 4 square root of 2 end cell end table end style

Jadi, panjang RS adalah begin mathsize 14px style 4 square root of 2 end style cm.

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