Pertanyaan

Segitiga ABC mempunyai panjang sisi a,b dan c . Jika a + b = 8 , ∠ A = 3 0 ∘ dan , panjang sisi b adalah ....

Segitiga $ABC$ mempunyai panjang sisi $a,b$ dan $c$ . Jika $a + b = 8, ∠ A = 3 0^{\circ}$ dan , panjang sisi $b$ adalah ....

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Habis dalam

Klaim

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Dengan menggunakan aturan sinus: Substitusi nilai : Jadi, jawaban yang tepat adalah C.

Dengan menggunakan aturan sinus:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator s i n space angle A end fraction end cell equals cell fraction numerator b over denominator s i n space angle B end fraction end cell row blank rightwards double arrow cell fraction numerator a over denominator s i n space 30 degree end fraction equals fraction numerator b over denominator s i n space 60 degree end fraction end cell row blank rightwards double arrow cell fraction numerator a over denominator open parentheses begin display style 1 half end style close parentheses end fraction equals fraction numerator b over denominator open parentheses begin display style fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses end fraction end cell row blank rightwards double arrow cell fraction numerator square root of 3 over denominator 2 end fraction a equals 1 half b end cell row blank rightwards double arrow cell square root of 3 a equals b end cell row blank rightwards double arrow cell a equals fraction numerator 1 over denominator square root of 3 end fraction b end cell end table end style$

Substitusi nilai :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a plus b end cell equals 8 row cell fraction numerator 1 over denominator square root of 3 end fraction b plus b end cell equals 8 row cell fraction numerator 1 plus square root of 3 over denominator square root of 3 end fraction b end cell equals 8 row b equals cell fraction numerator 8 square root of 3 over denominator 1 plus square root of 3 end fraction space left parenthesis kali space sekawan right parenthesis end cell row blank rightwards double arrow cell b equals fraction numerator 8 square root of 3 over denominator 1 plus square root of 3 end fraction cross times fraction numerator 1 minus square root of 3 over denominator 1 minus square root of 3 end fraction end cell row blank equals cell fraction numerator 8 square root of 3 minus 24 over denominator negative 2 end fraction end cell row blank equals cell 12 minus 4 square root of 3 end cell end table end style$

Jadi, jawaban yang tepat adalah C.