Roboguru

Diketahui segitiga  dengan  cm, , sudut , maka besar sudut  adalah ....

Pertanyaan

Diketahui segitiga ABC dengan AC equals 3 cm, BC equals 3 over 2 square root of 6, sudut straight A equals 60 degree, maka besar sudut straight C adalah ....

Pembahasan Soal:

Diketahui:

AC equals 3 space cm rightwards arrow straight b equals 3 space cm BC equals 3 over 2 square root of 6 space cm rightwards arrow straight a equals 3 over 2 square root of 6 space cm angle straight A equals 60 degree 

Maka berlaku:

space space space space fraction numerator straight a over denominator sin space straight A end fraction equals fraction numerator straight b over denominator sin space straight B end fraction equals fraction numerator straight c over denominator sin space straight C end fraction fraction numerator begin display style 3 over 2 end style square root of 6 over denominator sin space 60 degree end fraction equals fraction numerator 3 over denominator sin space straight B end fraction equals fraction numerator straight c over denominator sin space straight C end fraction 

Sehingga:

space space space space space space space space fraction numerator begin display style 3 over 2 square root of 6 end style over denominator sin space 60 degree end fraction equals fraction numerator 3 over denominator sin space straight B end fraction space space space space space space space space space space fraction numerator begin display style 3 over 2 square root of 6 end style over denominator begin display style 1 half end style square root of 3 end fraction equals fraction numerator 3 over denominator sin space straight B end fraction 3 over 2 square root of 6 cross times sin space straight B equals 1 half square root of 3 cross times 3 3 over 2 square root of 6 cross times sin space straight B equals 3 over 2 square root of 3 space space space space space space space space space space space space space sin space straight B equals fraction numerator begin display style 3 over 2 end style square root of 3 over denominator begin display style 3 over 2 end style square root of 6 end fraction space space space space space space space space space space space space space sin space straight B equals fraction numerator square root of 3 over denominator square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction space space space space space space space space space space space space space sin space straight B equals fraction numerator square root of 18 over denominator 6 end fraction space space space space space space space space space space space space space sin space straight B equals fraction numerator 3 square root of 2 over denominator 6 end fraction space space space space space space space space space space space space space sin space straight B equals 1 half square root of 2 space space space space space space space space space space space space space sin space straight B equals sin space 45 degree space space space space space space space space space space space space space space space space space space space straight B equals 45 degree 

Oleh karena itu:

angle straight A plus angle straight B plus angle straight C equals 180 degree space 60 degree plus 45 degree plus angle straight C equals 180 degree space space space space space space space space space 105 degree plus angle straight C equals 180 degree space space space space space space space space space space space space space space space space space space space space angle straight C equals 180 degree minus 105 degree space space space space space space space space space space space space space space space space space space space space angle straight C equals 75 degree 

Jadi, besar sudut straight C adalah 75 degree.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Juni 2021

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