Pertanyaan

Tentukan nilai x pada gambar berikut!

Tentukan nilai $x$ pada gambar berikut!

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Perhatikan gambar berikut! Menentukan besar sudut ADC Sudut ADC dan sudut ADB saling berpelurus, maka Menentukan panjang AD menggunakan aturan sinus Menentukan panjang BD = menggunakan definisi cos Jadi, nilai .

Perhatikan gambar berikut!

Menentukan besar sudut ADC

Sudut ADC dan sudut ADB saling berpelurus, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell angle ADC plus angle ADB end cell equals cell 180 degree end cell row cell angle ADC plus 60 degree end cell equals cell 180 degree end cell row cell angle ADC end cell equals cell 180 degree minus 60 degree end cell row cell angle ADC end cell equals cell 120 degree end cell end table

Menentukan panjang AD menggunakan aturan sinus

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AD over denominator sin space angle ACD end fraction end cell equals cell fraction numerator AC over denominator sin space angle ADC end fraction end cell row cell fraction numerator AD over denominator sin space 30 degree end fraction end cell equals cell fraction numerator 10 over denominator sin space 120 degree end fraction end cell row cell fraction numerator AD over denominator begin display style sin space 30 degree end style end fraction end cell equals cell fraction numerator 10 over denominator sin space left parenthesis 180 degree minus 60 degree right parenthesis end fraction end cell row cell fraction numerator AD over denominator begin display style sin space 30 degree end style end fraction end cell equals cell fraction numerator 10 over denominator sin space 60 degree end fraction end cell row cell fraction numerator AD over denominator begin display style 1 half end style end fraction end cell equals cell fraction numerator 10 over denominator begin display style 1 half end style square root of 3 end fraction end cell row AD equals cell fraction numerator 10 over denominator begin display style 1 half end style square root of 3 end fraction cross times 1 half end cell row AD equals cell fraction numerator 10 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row AD equals cell 10 over 3 square root of 3 end cell end table$

Menentukan panjang BD = menggunakan definisi cos

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space angle A D B end cell equals cell BD over AD end cell row cell cos space 60 degree end cell equals cell x over AD end cell row cell 1 half end cell equals cell fraction numerator x over denominator begin display style 10 over 3 end style square root of 3 end fraction end cell row cell 1 half times 10 over 3 square root of 3 end cell equals x row cell 5 over 3 square root of 3 end cell equals x end table$

Jadi, nilai x equals 5 over 3 square root of 3 .