Pertanyaan

Cermati Gambar berikut! Gambar 4.35 . Kombinasi segitiga siku-siku Dengan menemukan hubungan antarsudut-sudut dan panjang sisi-sisi pada segitiga siku-siku yang ada pada gambar, hitunglah sin 7 5 ∘ !

Cermati Gambar berikut!

Gambar 4.35. Kombinasi segitiga siku-siku

Dengan menemukan hubungan antarsudut-sudut dan panjang sisi-sisi pada segitiga siku-siku yang ada pada gambar, hitunglah $sin 7 5^{\circ}$ !

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style sin 75 degree equals DE over AD DE equals DF plus EF end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin 45 degree end cell equals cell DF over BD end cell row cell fraction numerator square root of 2 over denominator 2 end fraction end cell equals cell DF over BD end cell row DF equals cell fraction numerator square root of 2 over denominator 2 end fraction BD end cell end table end style$

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan 60 degree end cell equals cell AB over BD end cell row cell square root of 3 end cell equals cell AB over BD end cell row AB equals cell square root of 3 BD end cell row blank blank blank end table end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 45 degree end cell equals cell BC over AB end cell row cell fraction numerator square root of 2 over denominator 2 end fraction end cell equals cell BC over AB end cell row BC equals cell fraction numerator square root of 2 over denominator 2 end fraction AB end cell row EF equals cell BC equals fraction numerator square root of 2 over denominator 2 end fraction AB end cell end table end style$

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin 30 degree end cell equals cell BD over AD end cell row cell 1 half end cell equals cell BD over AD end cell row AD equals cell 2 BD end cell end table end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 75 degree end cell equals cell DE over AD end cell row blank equals cell fraction numerator DF plus EF over denominator AD end fraction end cell row blank equals cell fraction numerator fraction numerator square root of 2 over denominator 2 end fraction BD plus fraction numerator square root of 2 over denominator 2 end fraction AB over denominator 2 BD end fraction end cell row blank equals cell fraction numerator fraction numerator square root of 2 over denominator 2 end fraction BD plus fraction numerator square root of 2 over denominator 2 end fraction bullet square root of 3 BD over denominator 2 BD end fraction end cell row blank equals cell fraction numerator fraction numerator square root of 2 over denominator 2 end fraction plus fraction numerator square root of 6 over denominator 2 end fraction over denominator 2 end fraction end cell row blank equals cell fraction numerator 1 half open parentheses square root of 2 plus square root of 6 close parentheses over denominator 2 end fraction end cell row blank equals cell 1 fourth open parentheses square root of 2 plus square root of 6 close parentheses end cell end table end style$