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Perhatikan gambar berikut. Panjang tali busur AB adalah 6 cm dan sudut pusat AOB = 12 0 ∘ . Jika panjang BC = 4 cm, hitunglah besar sudut BOC.

Perhatikan gambar berikut.

Panjang tali busur AB adalah 6 cm dan sudut pusat AOB = . Jika panjang BC = 4 cm, hitunglah besar sudut BOC.

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F. Kartikasari

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

besar sudut BOC .

besar sudut BOCbegin mathsize 14px style equals 90 degree end style.

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Pembahasan

Segitiga AOB merupakan segitiga sama kaki karena AO = OB merupakan jari-jari lingkaran sehingga sudut A = sudut B. Jika , maka . Persamaan I Persamaan II Substitusi persamaan I ke persamaan II Jadi, besar sudut BOC .

Segitiga AOB merupakan segitiga sama kaki karena AO = OB merupakan jari-jari lingkaran sehingga sudut A = sudut B.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell angle straight A end cell equals cell fraction numerator 180 degree minus angle AOB over denominator 2 end fraction end cell row blank equals cell fraction numerator 180 degree minus 120 degree over denominator 2 end fraction end cell row blank equals cell fraction numerator 60 degree over denominator 2 end fraction end cell row blank equals cell 30 degree end cell end table end style

Jika begin mathsize 14px style angle BOC equals straight x degree end style, maka begin mathsize 14px style angle AOC equals open parentheses 120 minus straight x close parentheses degree end style.

Persamaan I

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator OC over denominator sin space angle CBO end fraction end cell equals cell fraction numerator BC over denominator sin space angle BOC end fraction end cell row cell fraction numerator OC over denominator sin space 30 degree end fraction end cell equals cell fraction numerator 4 over denominator sin space straight x degree end fraction end cell row OC equals cell fraction numerator 4 times begin display style 1 half end style over denominator sin space straight x degree end fraction end cell row OC equals cell fraction numerator 2 over denominator sin space straight x degree end fraction end cell end table end style

Persamaan II

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator OC over denominator sin space angle CAO space end fraction end cell equals cell fraction numerator AC over denominator sin space angle AOC end fraction end cell row cell fraction numerator OC over denominator sin space 30 degree end fraction end cell equals cell fraction numerator 6 minus 4 over denominator sin space open parentheses 120 minus straight x close parentheses degree end fraction end cell row OC equals cell fraction numerator 2 times begin display style 1 half end style over denominator sin space open parentheses 120 minus straight x close parentheses degree end fraction end cell row OC equals cell fraction numerator 1 over denominator sin space left parenthesis 120 minus straight x right parenthesis degree end fraction end cell end table end style

Substitusi persamaan I ke persamaan II

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 over denominator sin space straight x degree end fraction end cell equals cell fraction numerator 1 over denominator sin space open parentheses 180 minus open parentheses 120 minus straight x close parentheses close parentheses degree end fraction end cell row cell sin space straight x degree end cell equals cell 2 times sin space open parentheses 60 plus straight x close parentheses degree end cell row blank equals cell 2 times sin space 60 degree space cos space straight x degree plus 2 times cos space 60 degree space sin space straight x degree end cell row blank equals cell square root of 3 space cos space straight x degree plus sin space straight x degree end cell row cell square root of 3 space cos space straight x degree end cell equals 0 row straight x equals cell 90 degree end cell end table end style

Jadi, besar sudut BOCbegin mathsize 14px style equals 90 degree end style.

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