Pertanyaan

Diketahui segitiga PQR dengan PQ = 12 cm , PR = 8 cm , dan QR = 4 7 . Jika α adalah besar ∠ PQR , nilai tan α = ....

Diketahui segitiga PQR dengan $PQ = 12 cm$ , $PR = 8 cm$ , dan $QR = 47$ . Jika $α$ adalah besar $∠ PQR$ , nilai $tan α = ....$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Gambar segitiga PQR: Menghitung nilai cos pada sudut dengan menggunakan aturan cosinus: Menghitung panjang sisi segitiga siku-siku: a) Panjang QO: b) Panjang RO: Menghitung nilai tan : Jadi, jawaban yang tepat adalah B.

Gambar segitiga PQR:

Menghitung nilai cos pada sudut 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 alpha 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 PQ squared plus QR squared minus PR squared over denominator 2 times PQ times QR 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 alpha 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 left parenthesis 4 square root of 7 right parenthesis squared minus 8 squared over denominator 2 times 12 times left parenthesis 4 square root of 7 right parenthesis 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 alpha 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 112 minus 64 over denominator 96 square root of 7 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 alpha 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 192 over denominator 96 square root of 7 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 alpha 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 2 over denominator square root of 7 end fraction end cell 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 Q O over denominator Q R end fraction end cell end table end style$

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

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row QO equals cell fraction numerator 2 over denominator square root of 7 end fraction cross times text QR end text end cell row blank equals cell fraction numerator 2 over denominator square root of 7 end fraction cross times 4 square root of 7 space text cm end text end cell row blank equals cell 8 space text cm end text end cell end table end style$

b) Panjang RO:

Error converting from MathML to accessible text.

Menghitung nilai tan :

$begin mathsize 14px style tan space straight alpha equals QO over RO tan space straight alpha equals fraction numerator begin display style 4 square root of 3 end style over denominator 8 end fraction tan space straight alpha equals 1 half square root of 3 end style$

Jadi, jawaban yang tepat adalah B.