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Diketahui segitiga ABC siku-siku di sudut A. Jika ...

Diketahui segitiga ABC siku-siku di sudut A. Jika panjang sisi a equals 8 space d a n space b equals 4 text , end text maka perbandingan trigonometri yang benar adalah ... 

  1. cos space B equals 1 half square root of 3 comma space T a n space C equals 1 third square root of 3 

  2. cos space B equals 1 half square root of 3 comma space T a n space C equals 1 half 

  3. sin space B equals 1 half comma space sin space C equals 1 half square root of 3 

  4. sin space B equals 1 half square root of 3 comma space cos space B equals 1 third square root of 3 

  5. tan space B equals 1 half comma space cos space C equals 1 half 

Jawaban:

Gambar segitiga siku-siku ABC tersebut.

 

Panjang sisi c yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row c equals cell square root of a squared minus b squared end root end cell row blank equals cell square root of 8 squared minus 4 squared end root end cell row blank equals cell square root of 64 minus 16 end root end cell row blank equals cell square root of 48 end cell row blank equals cell 4 square root of 3 end cell end table 

Sehingga untuk sudut B diperoleh:

sin space B equals fraction numerator d e over denominator m i end fraction equals b over a equals 4 over 8 equals 1 half cos space B equals fraction numerator s a over denominator m i end fraction equals c over a equals fraction numerator 4 square root of 3 over denominator 8 end fraction equals 1 half square root of 3 tan space B equals fraction numerator d e over denominator s a end fraction equals b over c equals fraction numerator 4 over denominator 4 square root of 3 end fraction equals 1 third square root of 3blank 

Dan untuk sudut C diperoleh:

sin space C equals fraction numerator d e over denominator m i end fraction equals c over a equals fraction numerator 4 square root of 3 over denominator 8 end fraction equals 1 half square root of 3 cos space C equals fraction numerator s a over denominator m i end fraction equals b over a equals 4 over 8 equals 1 half tan space C equals fraction numerator d e over denominator s a end fraction equals c over b equals fraction numerator 4 square root of 3 over denominator 4 end fraction equals square root of 3 

Diperoleh jawaban yang sesuai yaitu sin space B equals 1 half comma space sin space C equals 1 half square root of 3

Oleh karena itu, jawaban yang benar adalah C. 

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