Roboguru

Pada segitiga ABC lancip diketahui  dan , maka

Pertanyaan

Pada segitiga ABC lancip diketahui cos space italic A equals 4 over 5 dan sin space B equals 12 over 13, maka sin space C equals....  

Pembahasan Soal:

Diketahui:

 table attributes columnalign right center left columnspacing 0px end attributes row cell sin space B end cell equals cell 12 over 13 end cell row cell cos space A end cell equals cell 4 over 5 end cell end table

Karena segitiga ABC lancip maka besar ketiga sudutnya angle 90 degree (kuadran I) sehingga nilai fungsi trigonometrinya selalu positif. Selanjutnya dapat ditentukan cos space B space dan space sin space italic A dengan identitas trigonometri sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row 1 equals cell sin squared space B plus cos squared space B end cell row cell cos italic space B end cell equals cell square root of 1 minus sign sin squared space B end root end cell row blank equals cell square root of 1 minus sign begin italic style left parenthesis 12 over 13 right parenthesis end style squared end root end cell row blank equals cell square root of 1 minus sign 144 over 169 end root end cell row blank equals cell square root of fraction numerator 169 minus sign 144 over denominator 169 end fraction end root end cell row blank equals cell square root of 25 over 169 end root end cell row blank equals cell 5 over 13 end cell row blank blank blank row 1 equals cell sin squared space italic A plus cos squared space italic A end cell row cell sin italic space italic A end cell equals cell square root of 1 minus sign cos squared space italic A end root end cell row blank equals cell square root of 1 minus sign begin italic style left parenthesis 4 over 5 right parenthesis end style squared end root end cell row blank equals cell square root of 1 minus sign 16 over 25 end root end cell row blank equals cell square root of fraction numerator 25 minus sign 16 over denominator 25 end fraction end root end cell row blank equals cell square root of 9 over 25 end root end cell row blank equals cell 3 over 5 end cell end table  

Karena jumlah besar sudut dalam suatu segitiga adalah 180 degree maka C equals 180 degree minus sign open parentheses italic A and B close parentheses. Sehingga dapat ditentukan nilai dari sin space C sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space C end cell equals cell sin space open parentheses 180 degree minus sign open parentheses italic A and B close parentheses close parentheses end cell row blank equals cell sin space 180 degree middle dot cos space left parenthesis italic A and B right parenthesis minus sign sin space left parenthesis italic A and B right parenthesis middle dot cos space 180 degree end cell row blank equals cell 0 middle dot cos space left parenthesis italic A and B right parenthesis minus sign sin space left parenthesis italic A and B right parenthesis middle dot open parentheses negative sign 1 close parentheses end cell row blank equals cell sin space left parenthesis italic A and B right parenthesis end cell row blank equals cell sin space italic A middle dot cos space B and sin space B middle dot cos space italic A end cell row blank equals cell 3 over 5 middle dot 5 over 13 plus 12 over 13 middle dot 4 over 5 end cell row blank equals cell fraction numerator 15 plus 48 over denominator 65 end fraction end cell row blank equals cell 63 over 65 end cell end table  

Dengan demikian nilai dari sin space C equals 63 over 65.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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