Pertanyaan

Diketahui segitiga ABC dengan panjang AB = 3 cm , BC = 6 3 cm , dan AC = 12 cm . Nilai sinus sudut A adalah . . . .

Diketahui segitiga ABC dengan panjang $AB = 3 cm$ , $BC = 63 cm$ , dan $AC = 12 cm$ . Nilai sinus sudut $A$ adalah . . . .

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Gambar segitiga: Menghitung nilai cos pada sudut A dengan menggunakan aturan cosinus: Menghitung panjang sisi segitiga siku-siku: a) Panjang AO: b) Panjang BO: Menghitung nilai sin A: Jadi, jawaban yang tepat adalah C.

Gambar segitiga:

Menghitung nilai cos pada sudut A dengan menggunakan aturan cosinus:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos 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 straight A 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 fraction numerator AC squared plus AB squared minus BC squared over denominator 2 times AC times AB end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos 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 straight A 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 fraction numerator 12 squared plus 3 squared minus left parenthesis 6 square root of 3 right parenthesis squared over denominator 2 times 12 times 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos 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 straight A 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 fraction numerator 144 plus 9 minus 108 over denominator 72 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos 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 straight A 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 45 over 72 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos 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 straight A 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 cell 5 over 8 end cell equals cell AO over AB end cell end table end style$

Menghitung panjang sisi segitiga siku-siku:
a) Panjang AO:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row AO equals cell 5 over 8 cross times AB end cell row blank equals cell 5 over 8 cross times 3 space text cm end text end cell row blank equals cell 15 over 8 space text cm end text end cell end table end style

b) Panjang BO:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row BO equals cell square root of 3 squared minus left parenthesis 15 over 8 right parenthesis squared end root end cell row BO equals cell square root of 9 minus 225 over 64 end root end cell row BO equals cell square root of fraction numerator 576 minus 225 over denominator 64 end fraction end root end cell row BO equals cell square root of 351 over 64 end root end cell row BO equals cell square root of fraction numerator 9 cross times 39 over denominator 64 end fraction end root end cell row BO equals cell 3 over 8 square root of 39 space text cm end text end cell end table end style$

Menghitung nilai sin A:

$begin mathsize 14px style sin space straight A equals BO over AB sin space straight A equals fraction numerator begin display style 3 over 8 square root of 39 end style over denominator 3 end fraction sin space straight A equals 1 over 8 square root of 39 end style$

Jadi, jawaban yang tepat adalah C.