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Hitunglah panjang sisi , jika sudut , sudut , dan ...

Hitunglah panjang sisi begin mathsize 14px style triangle ABC end style, jika sudut begin mathsize 14px style A space 30 degree end style, sudut begin mathsize 14px style C space 90 degree end style, dan panjang sisi begin mathsize 14px style BC equals 6 space cm end style

Jawaban:

Gambar segitiga tersebut yaitu:

 

begin mathsize 14px style straight m angle B equals 180 degree minus left parenthesis 90 degree plus 30 degree right parenthesis equals 60 degree end style 

Dengan memanfaatkan aturan sinus, diperoleh:

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 BC over denominator sin space straight A end fraction end cell row cell fraction numerator AC over denominator sin space 60 degree end fraction end cell equals cell fraction numerator 6 over denominator sin space 30 degree end fraction end cell row AC equals cell fraction numerator 6 times sin space 60 degree over denominator sin space 30 degree end fraction end cell row AC equals cell fraction numerator 6 times begin display style 1 half end style square root of 3 over denominator begin display style 1 half end style end fraction end cell row AC equals cell 6 square root of 3 end cell end table end style 

Dengan aturan sinus, akan ditentukan panjang sisi AB:

begin mathsize 14px style fraction numerator AB over denominator sin thin space straight C end fraction equals fraction numerator AC over denominator sin space straight B end fraction AB equals fraction numerator AC times sin thin space straight C over denominator sin space straight B end fraction AB equals fraction numerator 6 square root of 3 times sin space 90 degree over denominator sin space 60 degree end fraction AB equals fraction numerator 6 square root of 3 times 1 over denominator begin display style 1 half end style square root of 3 end fraction AB equals 12 space cm end style 

Jadi, panjang sisi segitiga tersebut yaitu begin mathsize 14px style bottom enclose bold AC bold equals bold 6 square root of bold 3 bold space bold cm bold space bold dan bold space bold AB bold equals bold 12 bold space bold cm end enclose end style.

 

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