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Penampang depan sebuah tenda berbentuk segitiga siku-siku sama kaki seperti tampak pada gambar. Jika lebar tenda 4 m. Hitungah keliling penampang tersebut!

Pertanyaan

Penampang depan sebuah tenda berbentuk segitiga siku-siku sama kaki seperti tampak pada gambar. Jika lebar tenda 4 m. Hitungah keliling penampang tersebut!undefined

  1. ...begin mathsize 14px style space end style 

  2. ...begin mathsize 14px style space end style 

Pembahasan Soal:


Karena segitiga ABC siku-siku sama kaki, maka AC = BC, AD = BD.
Untuk mencari keliling, pertama tentukan panjang sisi AC menggunakan atuan sinus
begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator A D over denominator sin space C end fraction end cell equals cell fraction numerator A C over denominator sin space D end fraction end cell row cell fraction numerator 2 over denominator sin space 45 degree end fraction end cell equals cell fraction numerator A C over denominator sin space 90 degree end fraction end cell row cell fraction numerator 2 over denominator begin display style bevelled 1 half end style square root of 2 end fraction end cell equals cell fraction numerator A C over denominator 1 end fraction end cell row cell A C end cell equals cell fraction numerator 4 over denominator square root of 2 end fraction end cell row cell A C end cell equals cell 2 square root of 2 end cell end table end style

Sehingga keliling segitiga tersebut
begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell K e l i l i n g end cell equals cell A B plus A C plus B C end cell row blank equals cell 4 plus 2 square root of 2 plus 2 square root of 2 end cell row blank equals cell 4 plus 2 square root of 2 end cell end table end style

Jadi keliling segitiga tersebut adalah size 14px 4 size 14px plus size 14px 2 square root of size 14px 2 size 14px space size 14px cm

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

L. Sibuea

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 05 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Perhatikan gambar berikut!   Ilustrator: Arif Nursahid Panjang sisi AB adalah ...

Pembahasan Soal:


Aturan sinus merupakan suatu aturan menyatakan hubungan perbandingan nilai sinus sudut-sudut dalam segitiga dengan panjang sisi yang berhadapan dengan sudut tersebut.

fraction numerator a over denominator sin space straight A end fraction equals fraction numerator b over denominator sin space straight B end fraction equals fraction numerator c over denominator sin space straight C end fraction 

Perhatikan segitiga BCD!

Tentukan panjang CD menggunakan aturan sinus. 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator CD over denominator sin space straight B end fraction end cell equals cell fraction numerator BC over denominator sin space straight D end fraction end cell row cell fraction numerator CD over denominator sin space 45 degree end fraction end cell equals cell fraction numerator 12 square root of 2 over denominator sin space 90 degree end fraction end cell row CD equals cell 12 square root of 2 times sin space 45 degree end cell row CD equals cell 12 square root of 2 times 1 half square root of 2 end cell row CD equals cell 12 space cm end cell end table 

Segitiga BCD merupakan segitiga sama kaki (salah satu besar sudutnya 45 degree), maka:

DB equals CD equals 12 space cm  

Perhatikan segitiga ACD!

Tentukan panjang AD menggunakan aturan sinus. 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AD over denominator sin space straight C end fraction end cell equals cell fraction numerator CD over denominator sin space straight A end fraction end cell row cell fraction numerator AD over denominator sin space open parentheses 180 degree minus 90 degree minus 60 degree close parentheses end fraction end cell equals cell fraction numerator 12 over denominator sin space 60 degree end fraction end cell row cell fraction numerator AD over denominator sin space 30 degree end fraction end cell equals cell fraction numerator 12 over denominator sin space 60 degree end fraction end cell row AD equals cell fraction numerator 12 over denominator sin space 60 degree end fraction times sin space 30 degree end cell row AD equals cell fraction numerator 12 over denominator begin display style 1 half end style square root of 3 end fraction times 1 half end cell row AD equals cell fraction numerator 12 over denominator square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row AD equals cell 4 square root of 3 space cm end cell end table 

Panjang sisi AB.

table attributes columnalign right center left columnspacing 0px end attributes row AB equals cell AD plus DB end cell row blank equals cell open parentheses 4 square root of 3 plus 12 close parentheses space cm end cell end table  

Sehingga, table attributes columnalign right center left columnspacing 0px end attributes row blank blank AB end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 4 square root of 3 plus 12 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cm end table.

Oleh karena itu, jawaban yang benar adalah D.

0

Roboguru

Hitunglah nilai tanR!

Pembahasan Soal:

Dengan  menggunakan aturan sinus diperoleh perbandingan

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator PQ over denominator sin space R end fraction end cell equals cell fraction numerator PR over denominator sin space Q end fraction end cell row cell fraction numerator 4 square root of 2 over denominator sin space R end fraction end cell equals cell fraction numerator 8 square root of 3 over denominator sin space 45 degree end fraction end cell row cell fraction numerator 4 square root of 2 over denominator sin space R end fraction end cell equals cell fraction numerator 8 square root of 3 over denominator begin display style 1 half end style square root of 2 end fraction end cell row cell sin space R end cell equals cell fraction numerator 4 square root of 2 times begin display style 1 half end style square root of 2 over denominator 8 square root of 3 end fraction end cell row cell sin space R end cell equals cell fraction numerator 4 over denominator 8 square root of 3 end fraction end cell row cell sin space R end cell equals cell fraction numerator 4 over denominator 8 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 cell sin space R end cell equals cell fraction numerator 4 square root of 3 over denominator 8 times 3 end fraction end cell row cell sin space R end cell equals cell fraction numerator square root of 3 over denominator 6 end fraction end cell end table

Dengan menggunakan definisi sinus didapat perbandingan sisi pada segitiga siku-siku sebagai berikut

space sin space R equals depan over miring equals fraction numerator square root of 3 over denominator 6 end fraction

Sehingga dapat gambar ilustrasi sebagai berikut

Dengan menggunakan rumus Phytagoras diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell square root of 6 squared minus open parentheses square root of 3 close parentheses squared end root end cell row blank equals cell square root of 36 minus 3 end root end cell row blank equals cell square root of 33 end cell end table

Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space R end cell equals cell depan over samping end cell row blank equals cell fraction numerator square root of 3 over denominator straight x end fraction end cell row blank equals cell fraction numerator square root of 3 over denominator square root of 33 end fraction end cell row blank equals cell fraction numerator square root of 1 over denominator square root of 11 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 11 end fraction cross times fraction numerator square root of 11 over denominator square root of 11 end fraction end cell row blank equals cell 1 over 11 square root of 11 end cell end table

Dengan demikian nilai tan space R adalah 1 over 11 square root of 11.

0

Roboguru

Diketahui segitiga ABC dengan panjang sisi AC=30cm, besar sudut A=60∘ dan sudut B=45∘. Panjang sisi BC adalah .... cm

Pembahasan Soal:

Aturan sinus merupakan aturan perbandingan suatu sisi pada segitiga dengan sudut diseberangnya.

Panjang sisi B C dapat diketahui dengan menggunakan aturan sinus.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space A over denominator B C end fraction end cell equals cell fraction numerator sin space B over denominator AC end fraction end cell row cell fraction numerator sin space 60 degree over denominator B C end fraction end cell equals cell fraction numerator sin space 45 degree over denominator 30 end fraction end cell row cell fraction numerator 1 half square root of 3 over denominator B C end fraction end cell equals cell fraction numerator 1 half square root of 2 over denominator 30 end fraction end cell row cell B C end cell equals cell fraction numerator 1 half square root of 3 cross times 30 over denominator 1 half square root of 2 end fraction end cell row cell B C end cell equals cell fraction numerator up diagonal strike 1 half end strike square root of 3 cross times 30 over denominator up diagonal strike 1 half end strike square root of 2 end fraction end cell row cell B C end cell equals cell fraction numerator 30 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 B C end cell equals cell fraction numerator 30 square root of 6 over denominator 2 end fraction end cell row cell B C end cell equals cell 15 square root of 6 space cm end cell end table

Maka, panjang sisi B C adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 15 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 6 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cm end table

0

Roboguru

Diketahui segitiga ABC dengan panjang sisi BC=92​cm,AC=12cm, dan sinC=66​​. Luas △ABC adalah ....

Pembahasan Soal:

Luas segitiga ABC begin mathsize 14px style open parentheses straight L subscript increment ABC end subscript close parentheses end style :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight L subscript increment ABC end subscript end cell equals cell 1 half open parentheses AC close parentheses open parentheses BC close parentheses open parentheses sin space straight C close parentheses end cell row cell straight L subscript increment ABC end subscript end cell equals cell 1 half open parentheses 12 space cm close parentheses open parentheses 9 square root of 2 space cm close parentheses open parentheses fraction numerator square root of 6 over denominator 6 end fraction close parentheses end cell row cell straight L subscript increment ABC end subscript end cell equals cell 9 square root of 12 space cm squared end cell row cell straight L subscript increment ABC end subscript end cell equals cell 18 square root of 3 space cm squared end cell end table end style  

0

Roboguru

Tentukan nilai x pada gambar berikut!

Pembahasan Soal:

Perhatikan gambar berikut!

 

Menentukan besar sudut ADC

Sudut ADC dan sudut ADB saling berpelurus, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell angle ADC plus angle ADB end cell equals cell 180 degree end cell row cell angle ADC plus 60 degree end cell equals cell 180 degree end cell row cell angle ADC end cell equals cell 180 degree minus 60 degree end cell row cell angle ADC end cell equals cell 120 degree end cell end table

Menentukan panjang AD menggunakan aturan sinus

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AD over denominator sin space angle ACD end fraction end cell equals cell fraction numerator AC over denominator sin space angle ADC end fraction end cell row cell fraction numerator AD over denominator sin space 30 degree end fraction end cell equals cell fraction numerator 10 over denominator sin space 120 degree end fraction end cell row cell fraction numerator AD over denominator begin display style sin space 30 degree end style end fraction end cell equals cell fraction numerator 10 over denominator sin space left parenthesis 180 degree minus 60 degree right parenthesis end fraction end cell row cell fraction numerator AD over denominator begin display style sin space 30 degree end style end fraction end cell equals cell fraction numerator 10 over denominator sin space 60 degree end fraction end cell row cell fraction numerator AD over denominator begin display style 1 half end style end fraction end cell equals cell fraction numerator 10 over denominator begin display style 1 half end style square root of 3 end fraction end cell row AD equals cell fraction numerator 10 over denominator begin display style 1 half end style square root of 3 end fraction cross times 1 half end cell row AD equals cell fraction numerator 10 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 AD equals cell 10 over 3 square root of 3 end cell end table  

Menentukan panjang BD = x menggunakan definisi cos

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space angle A D B end cell equals cell BD over AD end cell row cell cos space 60 degree end cell equals cell x over AD end cell row cell 1 half end cell equals cell fraction numerator x over denominator begin display style 10 over 3 end style square root of 3 end fraction end cell row cell 1 half times 10 over 3 square root of 3 end cell equals x row cell 5 over 3 square root of 3 end cell equals x end table 

Jadi, nilai x equals 5 over 3 square root of 3.

 

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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