Roboguru

Tentukan panjang sisi dan sudut yang belum diketahui dari segitiga-segitiga berikut: (c)

Pertanyaan

Tentukan panjang sisi dan sudut yang belum diketahui dari segitiga-segitiga berikut:

(c) space 

Pembahasan Soal:

Menentukan besar sudut C

equals 180 degree minus angle straight A minus angle straight B equals 180 degree minus 53 degree minus 37 degree equals 90 degree 

Menentukan panjang sisi AB

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator sin space straight A end fraction end cell equals cell fraction numerator c over denominator sin space straight C end fraction end cell row cell fraction numerator 6 over denominator sin space 53 degree end fraction end cell equals cell fraction numerator AB over denominator sin space 90 degree end fraction end cell row cell fraction numerator 6 over denominator 0 comma 8 end fraction end cell equals cell AB over 1 end cell row cell 0 comma 8 AB end cell equals 6 row AB equals cell fraction numerator 6 over denominator 0 comma 8 end fraction end cell row AB equals cell 7 comma 5 space cm end cell end table 

Jadi, panjang sisi AB = 7,5 cm dan besar sudut C = 90 degree.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

E. Lestari

Mahasiswa/Alumni Universitas Sebelas Maret

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Perhatikan gambar di bawah ini! PQRS siku-siku di Q dan S, panja=ng PQ=20cm ; QR=15cm dan besar sudut QPR= sudut RPS. Hitung niai sinus sudut SPQ

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell P R end cell equals cell square root of 20 squared plus 15 squared end root end cell row blank equals cell square root of 400 plus 225 end root end cell row blank equals cell square root of 625 end cell row blank equals 25 row blank blank blank row cell Sin space straight x end cell equals cell space depan over miring end cell row cell sin space straight x end cell equals cell 15 over 25 end cell row cell sin space straight x end cell equals cell 3 over 5 end cell row blank blank blank row cell angle Q P R space end cell equals cell space angle R P S end cell row cell angle S P Q end cell equals cell angle Q P R space plus space angle R P S end cell row cell angle S P Q end cell equals cell angle Q P R plus angle Q P R end cell row cell angle S P Q end cell equals cell 2 angle Q P R end cell row blank blank blank row cell sin space angle S P Q end cell equals cell 2 cross times 3 over 5 end cell row cell sin space angle S P Q end cell equals cell 6 over 5 end cell row blank blank blank end table

Jadi, niai sinus sudut S P Q space adalah 6 over 5.

0

Roboguru

Perhatikan gambar berikut. Panjang AC + panjang BC pada gambar berikut adalah....

Pembahasan Soal:

Rumus aturan sinus :

begin mathsize 14px style fraction numerator B C over denominator sin space A end fraction equals fraction numerator A C over denominator sin space B end fraction equals fraction numerator A B over denominator sin space C end fraction end style 

nilai begin mathsize 14px style a end style yaitu :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AC over denominator sin space B end fraction end cell equals cell fraction numerator BC over denominator sin space A end fraction end cell row cell fraction numerator 1 plus a over denominator sin space 45 degree end fraction end cell equals cell fraction numerator 1 minus a over denominator sin space 60 degree end fraction end cell row cell fraction numerator 1 plus a over denominator 1 half square root of 2 end fraction end cell equals cell fraction numerator 1 minus a over denominator 1 half square root of 3 end fraction end cell row cell fraction numerator 1 plus a over denominator square root of 2 end fraction end cell equals cell fraction numerator 1 minus a over denominator square root of 3 end fraction end cell row cell square root of 3 open parentheses 1 plus a close parentheses end cell equals cell square root of 2 left parenthesis 1 minus a right parenthesis end cell row cell square root of 3 plus square root of 3 a end cell equals cell square root of 2 minus square root of 2 a end cell row cell square root of 3 a plus square root of 2 a end cell equals cell square root of 2 minus square root of 3 end cell row cell a open parentheses square root of 3 plus square root of 2 close parentheses end cell equals cell square root of 2 minus square root of 3 end cell row a equals cell fraction numerator square root of 2 minus square root of 3 over denominator square root of 3 plus square root of 2 end fraction end cell row a equals cell fraction numerator square root of 2 minus square root of 3 over denominator square root of 3 plus square root of 2 end fraction cross times fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 minus square root of 2 end fraction end cell row a equals cell fraction numerator square root of 6 minus 2 minus 3 plus square root of 6 over denominator 3 minus square root of 6 plus square root of 6 minus 2 end fraction end cell row a equals cell negative 5 plus 2 square root of 6 end cell end table end style  

Sehingga panjang AC + Panjang BC yaitu :

begin mathsize 14px style panjang blank AC plus panjang blank BC equals 1 plus a plus 1 minus a panjang blank AC plus panjang blank BC equals 1 plus left parenthesis negative 5 plus 2 square root of 6 right parenthesis plus 1 minus left parenthesis negative 5 plus 2 square root of 6 right parenthesis panjang blank AC plus panjang blank BC equals 2 end style  

jadi, Jawaban yang tepat adalah A.

0

Roboguru

Perhatikan gambar segitiga ABC berikut! Panjang AC adalah ... cm.

Pembahasan Soal:

Menggunakan aturan sinus, diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator BC over denominator sin open parentheses angle A close parentheses end fraction end cell equals cell fraction numerator AC over denominator sin open parentheses angle B close parentheses end fraction end cell row cell fraction numerator 30 over denominator sin open parentheses 60 degree close parentheses end fraction end cell equals cell fraction numerator AC over denominator sin open parentheses 45 degree close parentheses end fraction end cell row cell fraction numerator 30 over denominator begin display style 1 half end style square root of 3 end fraction end cell equals cell fraction numerator AC over denominator begin display style 1 half end style square root of 2 end fraction end cell row cell fraction numerator 30 over denominator begin display style 1 half square root of 3 end style end fraction cross times 1 half square root of 2 end cell equals cell fraction numerator AC over denominator begin display style 1 half square root of 2 end style end fraction cross times 1 half square root of 2 end cell row cell fraction numerator 30 square root of 2 over denominator square root of 3 end fraction end cell equals AC row cell fraction numerator 30 square root of 2 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 equals AC row cell fraction numerator 30 square root of 6 over denominator 3 end fraction end cell equals AC row cell 10 square root of 6 end cell equals cell straight A C end cell end table end style

Jadi, jawaban yang tepat adalah C.undefined 

1

Roboguru

Perhatikan gambar berikut!    Panjang sisi a=...

Pembahasan Soal:

Dengan menggunakan aturan sinus perbandaingan panjang sisi segitiga, diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight a over denominator sin space 60 degree end fraction end cell equals cell fraction numerator 24 over denominator sin space 45 degree end fraction end cell row cell fraction numerator straight a over denominator begin display style 1 half end style square root of 3 end fraction end cell equals cell fraction numerator 24 over denominator begin display style 1 half end style square root of 2 end fraction end cell row cell fraction numerator straight a over denominator square root of 3 end fraction end cell equals cell fraction numerator 24 over denominator square root of 2 end fraction end cell row straight a equals cell fraction numerator 24 cross times square root of 3 over denominator square root of 2 end fraction end cell row straight a equals cell fraction numerator 24 square root of 3 over denominator square root of 2 end fraction end cell row straight a equals cell fraction numerator 24 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 straight a equals cell fraction numerator 24 square root of 6 over denominator 2 end fraction end cell row straight a equals cell 12 square root of 6 space cm end cell end table 

Dengan demikian, jawaban yang tepat adalah B.

0

Roboguru

Diketahui △ABC dengan panjang a=4cm, ∠A=50∘ dan ∠B=70∘ maka panjang c adalah ...

Pembahasan Soal:

Besar sudut C pada segitiga ABC dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell angle C end cell equals cell 180 degree minus angle A minus angle B end cell row blank equals cell 180 degree minus 50 degree minus 70 degree end cell row blank equals cell 60 degree end cell end table end style

Berdasarkan aturan sinus, panjang begin mathsize 14px style c end styledapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator c over denominator sin space C end fraction end cell equals cell fraction numerator a over denominator sin space A end fraction end cell row cell fraction numerator c over denominator sin space 60 degree end fraction end cell equals cell fraction numerator 4 over denominator sin space 50 degree end fraction end cell row c equals cell fraction numerator 4 over denominator sin space 50 degree end fraction times sin space 60 degree end cell row c equals cell fraction numerator 4 over denominator sin space 50 degree end fraction times 1 half square root of 3 end cell row c equals cell fraction numerator 2 square root of 3 over denominator sin space 50 degree end fraction end cell end table end style

Oleh karena itu, jawaban yang tepat adalah B.

0

Roboguru

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