Roboguru

Apabila  dan ,  dan  sudut lancip. Hitunglah: a.

Apabila begin mathsize 14px style sin space a equals 8 over 17 end style dan begin mathsize 14px style cos space beta equals 4 over 5 end stylebegin mathsize 14px style a end style dan begin mathsize 14px style beta end style sudut lancip. Hitunglah:

a. begin mathsize 14px style fraction numerator tan space a minus tan space beta over denominator 1 plus tan space a times tan beta end fraction end style 

Jawaban:

Dapat diilustrasikan sudut begin mathsize 14px style alpha end style dan begin mathsize 14px style beta end style sebagai berikut.

Jika sisi di samping sudut undefined adalah begin mathsize 14px style x end style dan sisi di depan sudut undefined adalah begin mathsize 14px style y end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row x equals cell square root of 17 squared minus 8 squared end root equals square root of 225 equals 15 end cell row y equals cell square root of 5 squared minus 4 squared end root equals square root of 9 equals 3 end cell end table end style

Sehingga :

begin mathsize 14px style tan space alpha equals 8 over 15 tan space beta equals 3 over 4 end style 

Dengan demikian:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space alpha minus tan space beta over denominator 1 plus tan space alpha space tan space beta end fraction end cell equals cell fraction numerator open parentheses begin display style 8 over 15 end style close parentheses minus open parentheses begin display style 3 over 4 end style close parentheses over denominator 1 plus open parentheses begin display style 8 over 15 end style close parentheses open parentheses begin display style 3 over 4 end style close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses negative begin display style 13 over 60 end style close parentheses over denominator 1 plus open parentheses begin display style 24 over 60 end style close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses negative begin display style 13 over 60 end style close parentheses over denominator open parentheses begin display style 84 over 60 end style close parentheses end fraction end cell row blank equals cell negative 13 over 84 end cell end table end style  

Dengan demikian, jawabannya adalah begin mathsize 14px style negative 13 over 84 end style.

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