Pertanyaan

Perhatikan gambar berikut. Panjang AC + panjang BC pada gambar berikut adalah....

Perhatikan gambar berikut.

Panjang $AC$ + panjang $BC$ pada gambar berikut adalah....

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Klaim

W. Wati

Master Teacher

Jawaban terverifikasi

Pembahasan

Rumus aturan sinus : nilai yaitu : Sehingga panjang AC + Panjang BC yaitu : jadi, Jawaban yang tepatadalah A.

Rumus aturan sinus :

$begin mathsize 14px style fraction numerator B C over denominator sin space A end fraction equals fraction numerator A C over denominator sin space B end fraction equals fraction numerator A B over denominator sin space C end fraction end style$

nilai yaitu :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AC over denominator sin space B end fraction end cell equals cell fraction numerator BC over denominator sin space A end fraction end cell row cell fraction numerator 1 plus a over denominator sin space 45 degree end fraction end cell equals cell fraction numerator 1 minus a over denominator sin space 60 degree end fraction end cell row cell fraction numerator 1 plus a over denominator 1 half square root of 2 end fraction end cell equals cell fraction numerator 1 minus a over denominator 1 half square root of 3 end fraction end cell row cell fraction numerator 1 plus a over denominator square root of 2 end fraction end cell equals cell fraction numerator 1 minus a over denominator square root of 3 end fraction end cell row cell square root of 3 open parentheses 1 plus a close parentheses end cell equals cell square root of 2 left parenthesis 1 minus a right parenthesis end cell row cell square root of 3 plus square root of 3 a end cell equals cell square root of 2 minus square root of 2 a end cell row cell square root of 3 a plus square root of 2 a end cell equals cell square root of 2 minus square root of 3 end cell row cell a open parentheses square root of 3 plus square root of 2 close parentheses end cell equals cell square root of 2 minus square root of 3 end cell row a equals cell fraction numerator square root of 2 minus square root of 3 over denominator square root of 3 plus square root of 2 end fraction end cell row a equals cell fraction numerator square root of 2 minus square root of 3 over denominator square root of 3 plus square root of 2 end fraction cross times fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 minus square root of 2 end fraction end cell row a equals cell fraction numerator square root of 6 minus 2 minus 3 plus square root of 6 over denominator 3 minus square root of 6 plus square root of 6 minus 2 end fraction end cell row a equals cell negative 5 plus 2 square root of 6 end cell end table end style$

Sehingga panjang AC + Panjang BC yaitu :

begin mathsize 14px style panjang blank AC plus panjang blank BC equals 1 plus a plus 1 minus a panjang blank AC plus panjang blank BC equals 1 plus left parenthesis negative 5 plus 2 square root of 6 right parenthesis plus 1 minus left parenthesis negative 5 plus 2 square root of 6 right parenthesis panjang blank AC plus panjang blank BC equals 2 end style

jadi, Jawaban yang tepat adalah A.