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Perhatikan gambar berikut!   Ilustrator: Arif Nursahid Panjang sisi AB adalah ...

Pertanyaan

Perhatikan gambar berikut!



 

Ilustrator: Arif Nursahid

Panjang sisi AB adalah ...space 

  1. open parentheses 2 square root of 2 plus 4 close parentheses space cm 

  2. open parentheses 2 square root of 2 plus 4 square root of 3 close parentheses space cm 

  3. open parentheses 2 square root of 3 plus 4 close parentheses space cm 

  4. open parentheses 4 square root of 3 plus 12 close parentheses space cm 

  5. open parentheses 6 square root of 3 plus 12 close parentheses space cm 

Pembahasan Soal:


Aturan sinus merupakan suatu aturan menyatakan hubungan perbandingan nilai sinus sudut-sudut dalam segitiga dengan panjang sisi yang berhadapan dengan sudut tersebut.

fraction numerator a over denominator sin space straight A end fraction equals fraction numerator b over denominator sin space straight B end fraction equals fraction numerator c over denominator sin space straight C end fraction 

Perhatikan segitiga BCD!

Tentukan panjang CD menggunakan aturan sinus. 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator CD over denominator sin space straight B end fraction end cell equals cell fraction numerator BC over denominator sin space straight D end fraction end cell row cell fraction numerator CD over denominator sin space 45 degree end fraction end cell equals cell fraction numerator 12 square root of 2 over denominator sin space 90 degree end fraction end cell row CD equals cell 12 square root of 2 times sin space 45 degree end cell row CD equals cell 12 square root of 2 times 1 half square root of 2 end cell row CD equals cell 12 space cm end cell end table 

Segitiga BCD merupakan segitiga sama kaki (salah satu besar sudutnya 45 degree), maka:

DB equals CD equals 12 space cm  

Perhatikan segitiga ACD!

Tentukan panjang AD menggunakan aturan sinus. 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AD over denominator sin space straight C end fraction end cell equals cell fraction numerator CD over denominator sin space straight A end fraction end cell row cell fraction numerator AD over denominator sin space open parentheses 180 degree minus 90 degree minus 60 degree close parentheses end fraction end cell equals cell fraction numerator 12 over denominator sin space 60 degree end fraction end cell row cell fraction numerator AD over denominator sin space 30 degree end fraction end cell equals cell fraction numerator 12 over denominator sin space 60 degree end fraction end cell row AD equals cell fraction numerator 12 over denominator sin space 60 degree end fraction times sin space 30 degree end cell row AD equals cell fraction numerator 12 over denominator begin display style 1 half end style square root of 3 end fraction times 1 half end cell row AD equals cell fraction numerator 12 over denominator square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row AD equals cell 4 square root of 3 space cm end cell end table 

Panjang sisi AB.

table attributes columnalign right center left columnspacing 0px end attributes row AB equals cell AD plus DB end cell row blank equals cell open parentheses 4 square root of 3 plus 12 close parentheses space cm end cell end table  

Sehingga, table attributes columnalign right center left columnspacing 0px end attributes row blank blank AB end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 4 square root of 3 plus 12 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cm end table.

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Juni 2021

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