Roboguru

Nilai dari ...


Nilai dari begin mathsize 14px style cos beta minus cos gamma plus tan beta equals end style... 

  1. begin mathsize 14px style 12 over 25 end style 

  2. begin mathsize 14px style 61 over 125 end style 

  3. begin mathsize 14px style 149 over 156 end style 

Jawaban:

Perhatikan gambar pada soal!

Panjang sisi begin mathsize 14px style AB equals 12 end style dan panjang sisi begin mathsize 14px style BC equals 13 end style

Cari panjang begin mathsize 14px style AC end style dengan menggunakan Teorema Pythagoras seperti berikut:

begin mathsize 14px style AC squared equals BC squared minus AB squared space space AC equals plus-or-minus square root of BC squared minus AB squared end root space space AC equals plus-or-minus square root of 13 squared minus 12 squared end root space space AC equals plus-or-minus square root of 169 minus 144 end root space space AC equals plus-or-minus square root of 25 space space AC equals plus-or-minus 5 space space AC equals 5 end style

Panjang sisi begin mathsize 14px style AC end style adalah begin mathsize 14px style 5 end style.

Akibatnya:

begin mathsize 14px style cos space beta equals 12 over 13 cos space gamma equals 5 over 13 tan space beta equals 5 over 12 end style 

Maka,

begin mathsize 14px style table attributes columnalign center center left end attributes row cell cos italic space beta minus cos italic space gamma plus tan space beta end cell equals cell AB over BC minus AC over BC plus AC over AB end cell row space equals cell open parentheses 12 over 13 minus 5 over 13 close parentheses plus 5 over 12 end cell row space equals cell 7 over 13 plus 5 over 12 end cell row space equals cell fraction numerator 84 plus 65 over denominator 156 end fraction end cell row space equals cell 149 over 156 end cell end table end style  

 Jadi, jawaban yang tepat adalah C.

0

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