Roboguru

Perhatikan gambar berikut! Jika  cm, panjang  adalah ....

Pertanyaan

Perhatikan gambar berikut!

Jika begin mathsize 14px style B D equals 4 end style cm, panjang begin mathsize 14px style A C end style adalah ....

  1. begin mathsize 14px style 9 comma 3 end style 

  2. begin mathsize 14px style 9 comma 5 end style 

  3. begin mathsize 14px style 9 comma 8 end style 

  4. begin mathsize 14px style 10 end style 

Pembahasan Video:

Pembahasan Soal:

Dari gambar yang diberikan, perhatikan begin mathsize 14px style increment BDA end style dan kita hitung:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell space space space tan space B end cell equals cell AD over BD end cell row cell tan space 60 degree end cell equals cell AD over 4 end cell row cell space space space space space space space square root of 3 end cell equals cell AD over 4 end cell row cell space space space space space space space space AD end cell equals cell 4 cross times square root of 3 end cell row cell space space space space space space space space AD end cell equals cell 4 square root of 3 end cell end table end style  

kemudian, kita perhatikan begin mathsize 14px style increment ADC end style dan kita hitung:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell space space space sin space C end cell equals cell AD over AC end cell row cell sin space 45 degree end cell equals cell fraction numerator 4 square root of 3 over denominator AC end fraction end cell row cell space space space fraction numerator square root of 2 over denominator 2 end fraction end cell equals cell fraction numerator 4 square root of 3 over denominator AC end fraction end cell row cell space space space space space AC end cell equals cell fraction numerator 2 cross times 4 square root of 3 over denominator square root of 2 end fraction end cell row cell space space space space space AC end cell equals cell fraction numerator 8 square root of 3 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row cell space space space space space AC end cell equals cell fraction numerator 8 square root of 6 over denominator 2 end fraction end cell row cell space space space space space AC end cell equals cell 4 square root of 6 end cell row cell space space space space space AC end cell equals cell 9 comma 79 end cell row cell space space space space space AC end cell equals cell 9 comma 8 end cell end table end style  

Jadi, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Freelancer7

Terakhir diupdate 03 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Perhatikan gambar berikut!     Hitunglah panjang , , , , dan !

Pembahasan Soal:

Gunakan konsep sudut istimewa trigonometri dan perbandingan sisi trigonometri.

table attributes columnalign right center left columnspacing 2px end attributes row cell sin space alpha end cell equals cell fraction numerator sisi space depan space alpha over denominator sisi space miring end fraction end cell row cell tan space alpha end cell equals cell fraction numerator sisi space depan space alpha over denominator sisi space samping space alpha end fraction end cell row cell tan space 30 degree end cell equals cell 1 third square root of 3 end cell row cell tan space 45 degree end cell equals 1 row cell sin space 30 degree end cell equals cell 1 half end cell row cell sin space 45 degree end cell equals cell 1 half square root of 2 end cell end table

*Menentukan panjang CD.

table attributes columnalign right center left columnspacing 2px end attributes row cell tan space 45 degree end cell equals cell fraction numerator sisi space depan space 45 degree over denominator sisi space damping space 45 degree end fraction end cell row 1 equals cell CD over BC end cell row 1 equals cell CD over 18 end cell row CD equals cell 18 space cm end cell end table

*Menentukan panjang AC.

table attributes columnalign right center left columnspacing 2px end attributes row cell tan space 30 degree end cell equals cell fraction numerator sisi space depan space 30 degree over denominator sisi space damping space 30 degree end fraction end cell row cell 1 third square root of 3 end cell equals cell CD over AC end cell row cell 1 third square root of 3 end cell equals cell 18 over AC end cell row AC equals cell fraction numerator 18 over denominator begin display style 1 third end style square root of 3 end fraction end cell row AC equals cell fraction numerator 18 over denominator begin display style fraction numerator square root of 3 over denominator 3 end fraction end style end fraction end cell row AC equals cell 18 cross times fraction numerator 3 over denominator square root of 3 end fraction end cell row AC equals cell fraction numerator 54 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row AC equals cell 54 over 3 square root of 3 end cell row AC equals cell 18 square root of 3 space cm end cell end table

*Menentukan panjang AD.

table attributes columnalign right center left columnspacing 2px end attributes row cell sin space 30 degree end cell equals cell fraction numerator sisi space depan space 30 degree over denominator sisi space miring end fraction end cell row cell 1 half end cell equals cell CD over AD end cell row cell 1 half end cell equals cell 18 over AD end cell row cell AD cross times 1 end cell equals cell 18 cross times 2 end cell row AD equals cell 36 space cm end cell end table

*Menentukan panjang BD.

table attributes columnalign right center left columnspacing 2px end attributes row cell sin space 45 degree end cell equals cell fraction numerator sisi space depan space 45 degree over denominator sisi space miring end fraction end cell row cell 1 half square root of 2 end cell equals cell CD over BD end cell row cell 1 half square root of 2 end cell equals cell 18 over BD end cell row BD equals cell fraction numerator 18 over denominator begin display style 1 half end style square root of 2 end fraction end cell row BD equals cell fraction numerator 18 over denominator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style end fraction end cell row BD equals cell 18 cross times fraction numerator 2 over denominator square root of 2 end fraction end cell row BD equals cell fraction numerator 36 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row BD equals cell 36 over 2 square root of 2 end cell row BD equals cell 18 square root of 2 space cm end cell end table

*Menemukan panjang AB.

table attributes columnalign right center left columnspacing 2px end attributes row AC equals cell AB plus BC end cell row cell 18 square root of 3 end cell equals cell AB plus 18 end cell row AB equals cell open parentheses 18 square root of 3 minus 18 close parentheses space cm end cell end table

Jadi, diperoleh panjang CDACADBD, dan AB berturut-turut adalah 18 space cm18 square root of 3 space cm36 space cm18 square root of 2 space cm, dan open parentheses 18 square root of 3 minus 18 close parentheses space cm.

0

Roboguru

Perhatikan gambar di bawah ini !   Jika BD = 4 cm, panjang AC adalah ....

Pembahasan Soal:

Berdasarkan gambar di atas dapat diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan 60 degree end cell equals cell AD over BD end cell row cell square root of 3 end cell equals cell AD over 4 end cell row AD equals cell 4 square root of 3 end cell end table end style 

Akibatnya

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin 45 degree end cell equals cell AD over AC end cell row cell fraction numerator square root of 2 over denominator 2 end fraction end cell equals cell fraction numerator 4 square root of 3 over denominator AC end fraction end cell row cell square root of 2 cross times AC end cell equals cell 4 square root of 3 cross times 2 end cell row AC equals cell fraction numerator 8 square root of 3 over denominator square root of 2 end fraction end cell row AC equals cell fraction numerator 8 square root of 3 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row AC equals cell fraction numerator 8 square root of 6 over denominator 2 end fraction end cell row AC equals cell 4 square root of 6 end cell row AC almost equal to cell 9 comma 8 end cell end table end style 

Jadi, jawaban yang tepat adalah C.space  

0

Roboguru

Nilai dari

Pembahasan Soal:

Ingat bahwa:

  • table attributes columnalign right center left columnspacing 0px end attributes row cell tan open parentheses 60 degree close parentheses end cell equals cell square root of 3 end cell row cell cos open parentheses 60 degree close parentheses end cell equals cell 1 half end cell row cell sin open parentheses 45 degree close parentheses end cell equals cell fraction numerator square root of 2 over denominator 2 end fraction end cell end table 

Sehingga:

fraction numerator tan open parentheses 60 degree close parentheses minus 2 cos open parentheses 60 degree close parentheses over denominator sin squared open parentheses 45 degree close parentheses end fraction equals fraction numerator square root of 3 minus 2 times 1 half over denominator open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses squared end fraction equals fraction numerator square root of 3 minus 2 times 1 half over denominator 1 half end fraction equals fraction numerator square root of 3 minus 1 over denominator 1 half end fraction equals fraction numerator open parentheses square root of 3 minus 1 close parentheses times 2 over denominator 1 end fraction equals 2 open parentheses square root of 3 minus 1 close parentheses 

Jadi, hasil dari fraction numerator tan open parentheses 60 degree close parentheses minus 2 cos open parentheses 60 degree close parentheses over denominator sin squared open parentheses 45 degree close parentheses end fraction equals 2 open parentheses square root of 3 minus 1 close parentheses.

0

Roboguru

Hitunglah nilai dari !

Pembahasan Soal:

Tentukan nilai dari masing-masing nilai trigonometri yang diketahui, sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 45 degree end cell equals cell 1 half square root of 2 end cell row cell sin space 90 degree end cell equals 1 row cell cos space 60 degree end cell equals cell 1 half end cell end table end style 

Dengan demikian:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space 45 degree plus sin space 90 degree over denominator cos space 60 degree end fraction end cell equals cell fraction numerator open parentheses begin display style 1 half end style square root of 2 close parentheses plus 1 over denominator open parentheses begin display style 1 half end style close parentheses end fraction end cell row blank equals cell square root of 2 plus 2 end cell end table end style    

Sehingga, begin mathsize 14px style fraction numerator tan space 45 degree plus sin space 90 degree over denominator cos space 60 degree end fraction equals square root of 2 plus 2 end style.

0

Roboguru

Cermati Gambar berikut! Gambar 4.35. Kombinasi segitiga siku-siku Dengan menemukan hubungan antarsudut-sudut dan panjang sisi-sisi pada segitiga siku-siku yang ada pada gambar, hitunglah !

Pembahasan Soal:

begin mathsize 14px style sin 75 degree equals DE over AD DE equals DF plus EF end style


begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin 45 degree end cell equals cell DF over BD end cell row cell fraction numerator square root of 2 over denominator 2 end fraction end cell equals cell DF over BD end cell row DF equals cell fraction numerator square root of 2 over denominator 2 end fraction BD end cell end table end style 


  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan 60 degree end cell equals cell AB over BD end cell row cell square root of 3 end cell equals cell AB over BD end cell row AB equals cell square root of 3 BD 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 sin invisible function application 45 degree end cell equals cell BC over AB end cell row cell fraction numerator square root of 2 over denominator 2 end fraction end cell equals cell BC over AB end cell row BC equals cell fraction numerator square root of 2 over denominator 2 end fraction AB end cell row EF equals cell BC equals fraction numerator square root of 2 over denominator 2 end fraction AB end cell end table end style


 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin 30 degree end cell equals cell BD over AD end cell row cell 1 half end cell equals cell BD over AD end cell row AD equals cell 2 BD end cell end table end style


begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 75 degree end cell equals cell DE over AD end cell row blank equals cell fraction numerator DF plus EF over denominator AD end fraction end cell row blank equals cell fraction numerator fraction numerator square root of 2 over denominator 2 end fraction BD plus fraction numerator square root of 2 over denominator 2 end fraction AB over denominator 2 BD end fraction end cell row blank equals cell fraction numerator fraction numerator square root of 2 over denominator 2 end fraction BD plus fraction numerator square root of 2 over denominator 2 end fraction bullet square root of 3 BD over denominator 2 BD end fraction end cell row blank equals cell fraction numerator fraction numerator square root of 2 over denominator 2 end fraction plus fraction numerator square root of 6 over denominator 2 end fraction over denominator 2 end fraction end cell row blank equals cell fraction numerator 1 half open parentheses square root of 2 plus square root of 6 close parentheses over denominator 2 end fraction end cell row blank equals cell 1 fourth open parentheses square root of 2 plus square root of 6 close parentheses end cell end table end style

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

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