Pertanyaan

Diketahui suatu segitiga ABC memiliki sisi sepanjang 10 cm , c = 5 cm dan besar sudut α = 5 0 ∘ . Tentukan sudut γ dan panjang sisi b !

Diketahui suatu segitiga $ABC$ memiliki sisi $a$ sepanjang $10 cm$ , $c = 5 cm$ dan besar sudut $α = 5 0^{\circ}$ . Tentukan sudut $γ$ dan panjang sisi $b$ !

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Jawaban terverifikasi

Jawaban

besar sudut .

besar sudut gamma equals 22 comma 5 degree comma space b equals 12 comma 45 space cm

Pembahasan

Jadi, besar sudut .

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator sin space alpha end fraction end cell equals cell fraction numerator b over denominator sin space beta end fraction equals fraction numerator c over denominator sin gamma end fraction end cell row cell fraction numerator a over denominator sin space alpha end fraction end cell equals cell fraction numerator c over denominator sin space gamma end fraction end cell row cell fraction numerator 10 over denominator sin space 50 degree end fraction end cell equals cell fraction numerator 5 over denominator sin space gamma end fraction end cell row cell 10 space sin space gamma end cell equals cell 5 space sin space 50 degree end cell row cell sin space y end cell equals cell fraction numerator 5 space sin space 50 degree over denominator 10 end fraction end cell row cell sin space y end cell equals cell 0 comma 38 end cell row y equals cell a r c sin space open parentheses 0 comma 38 close parentheses end cell row y equals cell 22 comma 5 degree end cell row cell angle beta end cell equals cell 180 degree minus open parentheses 50 degree plus 22 comma 5 degree close parentheses end cell row blank equals cell 180 degree minus 72 comma 5 degree end cell row blank equals cell 107 comma 5 degree end cell row cell fraction numerator a over denominator sin space alpha end fraction end cell equals cell fraction numerator b over denominator sin space beta end fraction end cell row cell fraction numerator 10 over denominator sin space 50 degree end fraction end cell equals cell fraction numerator b over denominator sin space 107 comma 5 degree end fraction end cell row cell b space sin space 50 degree end cell equals cell 10 space sin space 107 comma 5 degree end cell row b equals cell fraction numerator 10 space sin space 107 comma 5 degree over denominator sin space 50 degree end fraction end cell row blank equals cell 12 comma 45 space cm end cell end table$

Jadi, besar sudut gamma equals 22 comma 5 degree comma space b equals 12 comma 45 space cm .