Pertanyaan

Tentukan sisi dan sudut yang belum diketahui pada segitiga ABD !

Tentukan sisi dan sudut yang belum diketahui pada segitiga $ABD$ !

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Habis dalam

Klaim

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Dengan menggunakan konsep jumlah sudut dalam segitiga, maka: Sehingga, Selanjutnya, Jadi,

Dengan menggunakan konsep jumlah sudut dalam segitiga, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell angle ADB end cell equals cell 180 degree minus 30 degree minus 45 degree end cell row blank equals cell 105 degree end cell end table

Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight A over denominator sin space 30 degree end fraction end cell equals cell fraction numerator straight B over denominator sin space 45 degree end fraction end cell row cell fraction numerator straight A over denominator sin space 30 degree end fraction end cell equals cell fraction numerator 10 over denominator sin space 45 degree end fraction end cell row cell fraction numerator straight A over denominator begin display style 1 half end style end fraction end cell equals cell fraction numerator 10 over denominator begin display style 1 half end style square root of 2 end fraction end cell row straight A equals cell 5 cross times fraction numerator 2 over denominator square root of 2 end fraction end cell row blank equals cell fraction numerator 10 over denominator square root of 2 end fraction end cell row blank equals cell 5 square root of 2 end cell end table$

Selanjutnya,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight D over denominator sin space 105 degree end fraction end cell equals cell fraction numerator straight B over denominator sin space 45 degree end fraction end cell row cell fraction numerator straight D over denominator sin space 105 degree end fraction end cell equals cell fraction numerator 10 over denominator sin space 45 degree end fraction end cell row cell fraction numerator straight D over denominator begin display style 0 comma 966 end style end fraction end cell equals cell fraction numerator 10 over denominator begin display style 1 half square root of 2 end style end fraction end cell row straight D equals cell fraction numerator 10 cross times 0 comma 966 over denominator 0 comma 71 end fraction end cell row blank equals cell 13 comma 61 cm end cell end table$

Jadi,

angle ADB equals 105 degree AB equals 13 comma 61 cm BD equals 5 square root of 2 cm