Roboguru

Carilah panjang CD dan CE.

Pertanyaan


Carilah panjang CD dan CE.

Pembahasan Soal:


Aturan sinus merupakan suatu aturan menyatakan hubungan perbandingan nilai sinus sudut-sudut dalam segitiga dengan panjang sisi yang berhadapan dengan sudut tersebut.

fraction numerator a over denominator sin space straight A end fraction equals fraction numerator b over denominator sin space straight B end fraction equals fraction numerator c over denominator sin space straight C end fraction 

Jumlah sudut dalam segitiga adalah 180 degree.

Segitiga CDE merupakan segitiga siku-siku, maka besar angle straight E:

table attributes columnalign right center left columnspacing 0px end attributes row cell angle straight C plus angle straight D plus angle straight E end cell equals cell 180 degree end cell row cell angle straight E end cell equals cell 180 degree minus open parentheses angle straight C plus angle straight D close parentheses end cell row cell angle straight E end cell equals cell 180 degree minus open parentheses 45 degree plus 90 degree close parentheses end cell row cell angle straight E end cell equals cell 180 degree minus 135 degree end cell row cell angle straight E end cell equals cell 45 degree end cell end table 

Dengan menggunakan aturan sinus, maka panjang CD pada segitiga di atas:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator CD over denominator sin space straight E end fraction end cell equals cell fraction numerator DE over denominator sin space straight C end fraction end cell row cell fraction numerator CD over denominator sin space 45 degree end fraction end cell equals cell fraction numerator 6 over denominator sin space 45 degree end fraction end cell row CD equals 6 end table  

Panjang CE.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator CE over denominator sin space straight D end fraction end cell equals cell fraction numerator DE over denominator sin space straight C end fraction end cell row cell fraction numerator CE over denominator sin space 90 degree end fraction end cell equals cell fraction numerator 6 over denominator sin space 45 degree end fraction end cell row cell CE over 1 end cell equals cell fraction numerator 6 over denominator begin display style bevelled fraction numerator square root of 2 over denominator 2 end fraction end style end fraction end cell row CE equals cell fraction numerator 6 times 2 over denominator square root of 2 end fraction end cell row CE equals cell fraction numerator 12 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row CE equals cell 12 over 2 square root of 2 end cell row CE equals cell 6 square root of 2 end cell end table 

Jadi, CD equals 6 dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank CE end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 end cell end table.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 03 Juni 2021

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved