Roboguru

Diketahui segitiga ABC dengan besar sudut A adalah , sudut B adalah , dan panjang sisi AC sama dengan 10 cm. Panjang BC pada segitiga ABC tersebut adalah ...

Pertanyaan

Diketahui segitiga ABC dengan besar sudut A adalah 60 degree, sudut B adalah 45 degree, dan panjang sisi AC sama dengan 10 cm. Panjang BC pada segitiga ABC tersebut adalah ...

  1. 8 square root of 3 

  2. 6 square root of 6 

  3. 6 square root of 5 

  4. 5 square root of 6 

  5. 5 square root of 3 

Pembahasan Soal:

Untuk mencari panjang BC kita bisa menggunakan aturan sinus.

fraction numerator B C over denominator sin A end fraction equals fraction numerator A C over denominator sin B end fraction space space space space rightwards arrow space space space space fraction numerator B C over denominator sin 60 degree end fraction equals fraction numerator 10 over denominator sin 45 degree end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space B C equals fraction numerator 10 over denominator sin 45 degree end fraction cross times sin 60 degree bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space B C equals fraction numerator 10 over denominator 1 half square root of 2 end fraction cross times begin inline style 1 half end style begin inline style square root of 3 end style bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space B C equals fraction numerator 10 square root of 3 over denominator square root of 2 end fraction bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space B C equals fraction numerator 10 square root of 3 over denominator square root of 2 end fraction space cross times space fraction numerator square root of 2 over denominator square root of 2 end fraction bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space B C equals fraction numerator 10 square root of 6 over denominator 2 end fraction bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space B C equals 5 square root of 6  

Jadi. jawaban yang tepat adalah D.

 

 

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 06 Mei 2021

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