Pertanyaan

Diketahui segitiga ABC dengan sudut A = 3 0 ∘ , sudut B = 4 5 ∘ , dan sisi b = 12 cm . Tentukan: Sudut C Panjang a Panjang c

Diketahui segitiga ABC dengan sudut $A = 3 0^{\circ}$ , sudut $B = 4 5^{\circ}$ , dan sisi $b = 12 cm$ . Tentukan:

Sudut C
Panjang $a$
Panjang $c$

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

panjang adalah .

panjang

begin mathsize 14px style c space end style

adalah

begin mathsize 14px style open parentheses 6 square root of 3 plus 6 close parentheses space cm end style

Pembahasan

a. Jumlah sudut dalam segitiga adalah Maka, Jadi, besar sudut C adalah b. Menentukan panjang dengan aturan sinus. Jadi panjang adalah . c. Menentukan . sin 10 5 ∘ = = = = = sin ( 6 0 ∘ + 4 5 ∘ ) ( sin 6 0 ∘ ⋅ cos 4 5 ∘ ) + ( cos 6 0 ∘ ⋅ sin 4 5 ∘ ) ( 2 3 ⋅ 2 2 ) + ( 2 1 ⋅ 2 2 ) 4 6 + ( 4 2 ) 4 1 ( 6 + 2 ) Menentukan panjang dengan aturan sinus. Dengan demikian, panjang adalah .

a. Jumlah sudut dalam segitiga adalah begin mathsize 14px style 180 degree. end style Maka,

Jadi, besar sudut C adalah begin mathsize 14px style 105 degree. end style

b. Menentukan panjang begin mathsize 14px style a comma end style dengan aturan sinus.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator sin space straight A end fraction end cell equals cell fraction numerator b over denominator sin space straight B end fraction end cell row cell fraction numerator a over denominator sin space 30 degree end fraction end cell equals cell fraction numerator 12 over denominator sin space 45 degree end fraction end cell row cell a times sin space 45 degree end cell equals cell 12 times sin space 30 degree end cell row cell a times fraction numerator 1 over denominator square root of 2 end fraction end cell equals cell 12 times 1 half end cell row cell a times fraction numerator 1 over denominator square root of 2 end fraction end cell equals 6 row a equals cell 6 times fraction numerator square root of 2 over denominator 1 end fraction end cell row a equals cell square root of 6 end cell end table end style$

Jadi panjang begin mathsize 14px style a space end style adalah begin mathsize 14px style square root of 6 space cm end style .

c. Menentukan begin mathsize 14px style sin space 105 degree end style .

$sin 10 5^{\circ} = = = = = sin (6 0^{\circ} + 4 5^{\circ}) (sin 6 0^{\circ} \cdot cos 4 5^{\circ}) + (cos 6 0^{\circ} \cdot sin 4 5^{\circ}) (\frac{3}{2} \cdot \frac{2}{2}) + (\frac{1}{2} \cdot \frac{2}{2}) \frac{6}{4} + (\frac{2}{4}) \frac{1}{4} (6 + 2)$

Menentukan panjang begin mathsize 14px style c comma end style dengan aturan sinus.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator b over denominator sin space straight B end fraction end cell equals cell fraction numerator c over denominator sin space straight C end fraction end cell row cell fraction numerator 12 over denominator sin space 45 degree end fraction end cell equals cell fraction numerator c over denominator sin space 105 degree end fraction end cell row cell c times sin space 45 degree end cell equals cell 12 times sin space 105 degree end cell row cell c times fraction numerator 1 over denominator square root of 2 end fraction end cell equals cell 12 times 1 fourth open parentheses square root of 6 plus square root of 2 close parentheses end cell row cell c times fraction numerator 1 over denominator square root of 2 end fraction end cell equals cell 3 open parentheses square root of 6 plus square root of 2 close parentheses end cell row c equals cell 3 open parentheses square root of 6 plus square root of 2 close parentheses times fraction numerator square root of 2 over denominator 1 end fraction end cell row c equals cell 3 square root of 2 open parentheses square root of 6 plus square root of 2 close parentheses end cell row c equals cell 3 square root of 12 plus 3 square root of 4 end cell row c equals cell 3 square root of 4 times 3 end root plus 3 times 2 end cell row c equals cell 3 times 2 square root of 3 plus 6 end cell row c equals cell 6 square root of 3 plus 6 end cell end table end style$

Dengan demikian, panjang begin mathsize 14px style c space end style adalah begin mathsize 14px style open parentheses 6 square root of 3 plus 6 close parentheses space cm end style .