Roboguru

Perhatikan gambar berikut. Nilai , ,  dan  adalah ....

Pertanyaan

Perhatikan gambar berikut.



Nilai begin mathsize 14px style sin space alpha end stylebegin mathsize 14px style cos space alpha end stylebegin mathsize 14px style sin space 2 alpha end style dan begin mathsize 14px style tan space 2 alpha end style adalah ....

Pembahasan Soal:

Menentukan panjang AC dengan Teorema Pythagoras.

   blankbegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row AC equals cell square root of AB squared plus BC squared end root end cell row blank equals cell square root of 5 squared plus left parenthesis square root of 11 right parenthesis squared end root end cell row blank equals cell square root of 25 plus 11 end root end cell row blank equals cell square root of 36 end cell row blank equals 6 end table end style  

Menentukan panjang AD dengan Teorema Pythagoras.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row AD equals cell square root of AB squared plus BD squared end root end cell row blank equals cell square root of 5 squared plus open parentheses square root of 11 plus 12 minus square root of 11 close parentheses squared end root end cell row blank equals cell square root of 5 squared plus 12 squared end root end cell row blank equals cell square root of 25 plus 144 end root end cell row blank equals cell square root of 169 end cell row blank equals 13 end table end style 

Menentukan nilai begin mathsize 14px style sin space alpha end stylebegin mathsize 14px style cos space alpha end stylebegin mathsize 14px style sin space 2 alpha end style dan begin mathsize 14px style tan space 2 alpha end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space alpha end cell equals cell BC over AC equals fraction numerator square root of 11 over denominator 6 end fraction equals 1 over 6 square root of 11 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 cos space alpha end cell equals cell AB over AC equals 5 over 6 end cell end table end style    

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 2 alpha end cell equals cell BD over AD equals 12 over 13 end cell end table end style   

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 2 alpha end cell equals cell BD over AB equals 12 over 5 end cell end table end style   

Jadi, nilai begin mathsize 14px style sin space alpha equals 1 over 6 square root of 11 end stylebegin mathsize 14px style cos space alpha equals 5 over 6 end stylebegin mathsize 14px style sin space 2 alpha equals 12 over 13 end style dan begin mathsize 14px style tan space 2 alpha equals 12 over 5 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 April 2021

Ruangguru

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