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Pada segitiga ABC dan ABD di atas jika sisi  dan  maka besar  adalah ...

Pertanyaan


Pada segitiga ABC dan ABD di atas jika sisi begin mathsize 14px style AC equals 8 square root of 3 space cm end style dan begin mathsize 14px style DC equals 8 space cm end style maka besar begin mathsize 14px style angle beta end style adalah ...

  1. begin mathsize 14px style 15 degree end style 

  2. begin mathsize 14px style 20 degree end style 

  3.  begin mathsize 14px style 30 degree end style 

  4. begin mathsize 14px style 35 degree end style

  5. begin mathsize 14px style 45 degree end style

Pembahasan Soal:

Perhatikan segitiga ABC dengan menggunakan definisi sinus maka diperoleh panjang DB:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 60 degree end cell equals cell BC over AC end cell row cell fraction numerator square root of 3 over denominator 2 end fraction end cell equals cell fraction numerator 8 plus DB over denominator 8 square root of 3 end fraction end cell row cell 2 open parentheses 8 plus DB close parentheses end cell equals cell 8 square root of 3 cross times square root of 3 end cell row cell 16 plus 2 DB end cell equals 24 row cell 2 DB end cell equals cell 24 minus 16 end cell row cell 2 DB end cell equals 8 row DB equals cell 4 space cm end cell end table end style 

Dengan menggunakan definisi tangen maka diperoleh panjang AB:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 60 degree end cell equals cell BC over AB end cell row cell square root of 3 end cell equals cell fraction numerator CD plus DB over denominator AB end fraction end cell row cell square root of 3 end cell equals cell fraction numerator 8 plus 4 over denominator AB end fraction end cell row cell square root of 3 AB end cell equals 12 row AB equals cell fraction numerator 12 over denominator square root of 3 end fraction end cell row AB equals cell fraction numerator 12 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row AB equals cell 4 square root of 3 end cell end table end style 

Perhatikan segitiga ABD dengan menggunakan definisi tangen maka diperoleh begin mathsize 14px style angle beta end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space beta end cell equals cell fraction numerator D B over denominator A B end fraction end cell row cell tan space beta end cell equals cell fraction numerator 4 over denominator 4 square root of 3 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row cell tan space beta end cell equals cell 1 third square root of 3 end cell row beta equals cell 30 degree end cell end table end style 

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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