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Suatu segitiga ABC siku-siku di B, jika sin C=32​ dan Panjang sisi AB=10​ cm, tentukan Panjang sisi segitiga yang lain dan nilai perbandingan trigonometri lainnya.

Pertanyaan

Suatu segitiga ABC siku-siku di B, jika sin space straight C equals 2 over 3 dan Panjang sisi AB equals square root of 10 space cm, tentukan Panjang sisi segitiga yang lain dan nilai perbandingan trigonometri lainnya.

R. Risda

Master Teacher

Jawaban terverifikasi

Jawaban

panjang BC equals 5 over 2 square root of 2 space cmAC equals 3 over 2 square root of 10 space cmcos space C equals 1 third square root of 5tan space C equals 2 over 5 square root of 5csc space straight C equals 3 over 2sec space straight C equals 3 over 5 square root of 5 dan ctg space straight C equals 1 half square root of 5

Pembahasan

Perbandingan nilai trigonometri pada segitiga siku-siku.

segitiga ABC siku-siku di B maka AC sisi miring.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight C end cell equals cell fraction numerator sisi space depan space straight C over denominator sisi space miring end fraction end cell row cell 2 over 3 end cell equals cell AB over AC end cell row cell 2 over 3 end cell equals cell fraction numerator square root of 10 space cm over denominator AC end fraction end cell row AC equals cell fraction numerator 3 square root of 10 over denominator 2 end fraction space cm end cell row blank blank blank end table 

Dengan teorema pythagoras:

table attributes columnalign right center left columnspacing 0px end attributes row BC equals cell square root of AC squared minus AB squared end root end cell row blank equals cell square root of left parenthesis 3 over 2 square root of 10 right parenthesis squared minus left parenthesis square root of 10 right parenthesis squared end root end cell row blank equals cell square root of 9 over 4 times 10 minus 10 end root end cell row blank equals cell square root of 90 over 4 minus 40 over 4 end root end cell row blank equals cell square root of 50 over 4 end root end cell row blank equals cell 1 half square root of 50 end cell row blank equals cell 1 half square root of 2 times 25 end root end cell row blank equals cell 5 over 2 square root of 2 space cm end cell end table 

Perbandingan trigonometeri lainnya:

  • Cos C yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight C end cell equals cell fraction numerator sisi space samping space straight C over denominator sisi space miring end fraction end cell row blank equals cell BC over AC end cell row blank equals cell fraction numerator begin display style 5 over 2 square root of 2 end style over denominator begin display style 3 over 2 square root of 10 end style end fraction end cell row blank equals cell fraction numerator 5 square root of 2 over denominator 3 square root of 10 end fraction end cell row blank equals cell fraction numerator 5 square root of 2 over denominator 3 square root of 10 end fraction cross times fraction numerator square root of 10 over denominator square root of 10 end fraction end cell row blank equals cell fraction numerator 5 square root of 20 over denominator 30 end fraction end cell row blank equals cell fraction numerator 5 square root of 4 cross times 5 end root over denominator 30 end fraction end cell row blank equals cell fraction numerator 10 square root of 5 over denominator 30 end fraction end cell row blank equals cell 1 third square root of 5 end cell end table 

  • tan C yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight C end cell equals cell fraction numerator sin space straight C over denominator cos space straight C end fraction end cell row blank equals cell fraction numerator begin display style 2 over 3 end style over denominator begin display style 1 third square root of 5 end style end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 5 end fraction end cell row blank equals cell 2 over 5 square root of 5 end cell end table 

  • Cosec C yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell cosec space straight C end cell equals cell fraction numerator 1 over denominator sin space straight C end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 2 over 3 end style end fraction end cell row blank equals cell 3 over 2 end cell end table 

  • Secan C yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell sec space straight C end cell equals cell fraction numerator 1 over denominator cos space straight C end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator square root of 5 over denominator 3 end fraction end style end fraction end cell row blank equals cell fraction numerator 3 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 3 cross times square root of 5 over denominator square root of 5 cross times square root of 5 end fraction end cell row blank equals cell 3 over 5 square root of 5 end cell end table 

  • Cotangen C yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell cot space straight C end cell equals cell fraction numerator 1 over denominator tan space straight C end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator 2 over denominator square root of 5 end fraction end style end fraction end cell row blank equals cell fraction numerator square root of 5 over denominator 2 end fraction end cell row blank equals cell 1 half square root of 5 end cell end table 

Dengan demikian, panjang BC equals 5 over 2 square root of 2 space cmAC equals 3 over 2 square root of 10 space cmcos space C equals 1 third square root of 5tan space C equals 2 over 5 square root of 5csc space straight C equals 3 over 2sec space straight C equals 3 over 5 square root of 5 dan ctg space straight C equals 1 half square root of 5

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