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Perhatikan gambar. Gunakan sifat-sifat segitiga khusus/istimewa untuk mengerjakan soal berikut! Diketahui besar sudut begin mathsize 14px style straight C equals 60 degree end style, besar sudut begin mathsize 14px style straight A equals 30 degree end style, dan panjang begin mathsize 14px style BD equals 3 space cm end style. Hitung panjang begin mathsize 14px style AC end style.

 

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Lihat segitiga ABD

begin mathsize 14px style angle straight A equals 30 degree end style begin mathsize 14px style angle B equals 60 degree end style begin mathsize 14px style angle straight D equals 90 degree end style
begin mathsize 14px style straight x equals BD end style  begin mathsize 14px style straight x square root of 3 equals AD end style   begin mathsize 14px style 2 straight x equals AB end style  
begin mathsize 14px style 3 space cm end style  begin mathsize 14px style 3 square root of 3 space cm end style  begin mathsize 14px style 6 space cm end style 

Lihat segitiga BDC

begin mathsize 14px style angle straight B equals 30 degree end style  begin mathsize 14px style angle straight C equals 60 degree end style  begin mathsize 14px style angle straight D equals 90 degree end style
begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row DC equals cell straight x square root of 3 equals 3 end cell row straight x equals cell fraction numerator 3 over denominator square root of 3 end fraction equals square root of 3 end cell row blank blank blank end table end style  begin mathsize 14px style 3 space cm equals BD end style    begin mathsize 14px style BC equals 2 square root of 3 end style 

begin mathsize 14px style AC equals AD plus DC equals 3 square root of 3 plus square root of 3 equals 4 square root of 3 end style  

Jadi, panjang AC adalah begin mathsize 14px style 4 square root of 3 end style.

 

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