RoboguruRoboguru
SD

Perhatikan gambar di samping, tentukan : sin A=...

Pertanyaan

Perhatikan gambar di samping,

tentukan : sin space straight A equals... 

H. Hermawan

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

nilai sin space straight A adalah 5 over 2 square root of 2 over 13 end root.

Pembahasan

Gunakan aturan sinus untuk mencari nilai sin space straight A

Pertama, cari panjang rusuk a atau BC dengan aturan cosinus:

table attributes columnalign right center left columnspacing 0px end attributes row cell AB squared end cell equals cell AC squared plus BC squared minus 2 cross times AC cross times BC cross times cos space 45 degree end cell row cell open parentheses 2 square root of 13 close parentheses squared end cell equals cell open parentheses 4 square root of 2 close parentheses squared plus straight a squared minus 8 square root of 2 cross times straight a cross times fraction numerator square root of 2 over denominator 2 end fraction end cell row 52 equals cell 32 plus straight a squared minus 8 straight a end cell row cell negative straight a squared plus 8 straight a plus 20 end cell equals 0 row cell open parentheses straight a plus 2 close parentheses open parentheses negative straight a plus 10 close parentheses end cell equals 0 end table

Sehingga panjang a adalah straight a equals negative 2 space cm space atau space straight a equals 10 space cm. Ambil nilai a positif yaitu straight a equals 10 space cm.

Selanjutnya, untuk mencari nilai sin space straight A gunakan aturan sinus yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator BC over denominator sin space straight A end fraction end cell equals cell fraction numerator AB over denominator sin space straight C end fraction end cell row cell fraction numerator 10 over denominator sin space straight A end fraction end cell equals cell fraction numerator 2 square root of 13 over denominator sin space 45 degree end fraction end cell row cell sin space straight A end cell equals cell fraction numerator 10 cross times begin display style fraction numerator square root of 2 over denominator 2 end fraction end style over denominator 2 square root of 13 end fraction end cell row cell sin space straight A end cell equals cell fraction numerator 5 square root of 2 over denominator 2 square root of 13 end fraction end cell row cell sin space straight A end cell equals cell 5 over 2 square root of 2 over 13 end root. end cell end table 

Dengan demikian, nilai sin space straight A adalah 5 over 2 square root of 2 over 13 end root.

15

0.0 (0 rating)

Pertanyaan serupa

Diketahui segi empat ABCD dengan AD=3 cm,  BC=5 cm, DC=4 cm, ∠BAD=90∘, dan ∠ABD=30∘  maka cos ∠BCD adalah ...

200

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia