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Segitiga ABC siku-siku di B. Jika panjang AC adala...

Segitiga ABC siku-siku di B. Jika panjang AC adalah begin mathsize 14px style 8 space cm end style dan begin mathsize 14px style angle straight A equals 30 degree end style. Htunglah panjang AB dan BC.

  1. begin mathsize 14px style... end style 

  2. begin mathsize 14px style... end style  

Jawaban:

untuk mencari AB dan BC, gunakan aturan sinus.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AC over denominator sin space straight B end fraction end cell equals cell fraction numerator AB over denominator sin space straight C end fraction end cell row cell fraction numerator 8 over denominator sin space 90 degree end fraction end cell equals cell fraction numerator AB over denominator sin space left parenthesis 180 degree minus left parenthesis 90 degree plus 30 degree right parenthesis right parenthesis end fraction end cell row cell fraction numerator 8 over denominator sin space 90 degree end fraction end cell equals cell fraction numerator AB over denominator sin space 60 degree end fraction end cell row cell 8 over 1 end cell equals cell fraction numerator AB over denominator begin display style fraction numerator square root of 3 over denominator 2 end fraction end style end fraction end cell row AB equals cell space 4 square root of 3 space cm end cell row cell fraction numerator AC over denominator sin space straight B end fraction end cell equals cell fraction numerator BC over denominator sin space straight A end fraction end cell row cell fraction numerator 8 over denominator sin space 90 degree end fraction end cell equals cell fraction numerator BC over denominator sin space 30 degree end fraction end cell row cell 8 over 1 end cell equals cell fraction numerator BC over denominator begin display style 1 half end style end fraction end cell row BC equals cell space 4 space cm end cell row blank blank blank row blank blank blank end table end style  

Jadi, panjang AB dan BC berturut-turut adalah begin mathsize 14px style 4 square root of 3 space cm space dan space 4 space cm end style.

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