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Diketahui  sudut lancip. Jika , nilai adalah ....

Diketahui begin mathsize 14px style straight P end style sudut lancip. Jika begin mathsize 14px style tan space straight P equals fraction numerator 5 square root of 11 over denominator 11 end fraction end style, nilai begin mathsize 14px style sin space straight P end styleadalah ....

  1. begin mathsize 14px style fraction numerator 5 over denominator square root of 11 end fraction end style 

  2. begin mathsize 14px style fraction numerator 6 over denominator square root of 11 end fraction end style  

  3. begin mathsize 14px style 5 over 6 end style  

  4. begin mathsize 14px style fraction numerator square root of 11 over denominator 5 end fraction end style  

  5. begin mathsize 14px style fraction numerator square root of 11 over denominator 6 end fraction end style 

Jawaban:

Gunakan konsep tangen dan sinus pada perbandingan sisi trigonometri pada segitiga siku-siku.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell tan space straight P end cell equals cell fraction numerator sisi space depan over denominator sisi space samping end fraction end cell row cell sin space straight P end cell equals cell fraction numerator sisi space depan over denominator sisi space miring end fraction end cell end table end style 

Asumsikan bawah sudut begin mathsize 14px style straight P end style merupakan salah satu sudut pada segitiga siku-siku.

Diketahui begin mathsize 14px style straight P end style sudut lancip. Jika begin mathsize 14px style tan space straight P equals fraction numerator 5 square root of 11 over denominator 11 end fraction end style.

Akan ditentukan nilai begin mathsize 14px style sin space straight P end style.

Terlebih dahulu tentukan ukuran panjang sisi miring, misalkan begin mathsize 14px style x end style.

begin mathsize 14px style tan space straight P equals fraction numerator 5 square root of 11 over denominator 11 end fraction equals fraction numerator sisi space depan over denominator sisi space samping end fraction end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell sisi space miring end cell equals cell square root of open parentheses sisi space depan close parentheses squared plus open parentheses sisi space samping close parentheses squared end root end cell row blank equals cell square root of open parentheses 5 square root of 11 close parentheses squared plus 11 squared end root end cell row blank equals cell square root of 275 plus 121 end root end cell row blank equals cell square root of 396 end cell row cell sisi space miring end cell equals cell 6 square root of 11 end cell end table end style 

Sehingga nilai begin mathsize 14px style sin space straight P end style dapat dihitung sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell sin space straight P end cell equals cell fraction numerator sisi space depan over denominator sisi space miring end fraction end cell row blank equals cell fraction numerator 5 up diagonal strike square root of 11 end strike over denominator 6 up diagonal strike square root of 11 end strike end fraction end cell row cell sin space straight P end cell equals cell 5 over 6 end cell end table end style 

Jadi, jawaban yang tepat adalah C.

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