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Tentukan besar sudut  pada setiap segitiga berikut...

Tentukan besar sudut begin mathsize 14px style theta end style pada setiap segitiga berikut, kemudian tentukan nilai sinus, cosinus, tangen, cosecant, secan, dan cotangent nya:

Jawaban:

Dengan Teorema pythagoras:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Panjang space sisi space depan space straight theta end cell equals cell square root of left parenthesis 65 space cm right parenthesis squared minus left parenthesis 40 space cm right parenthesis squared end root end cell row blank equals cell square root of 4.225 space cm squared space minus space 1.600 space cm squared end root end cell row blank equals cell square root of 2.625 space cm squared end root end cell row blank equals cell square root of 25 times 105 end root space cm end cell row blank equals cell 5 square root of 105 space cm end cell end table end style 

Maka perbandingan trigonometrinya adalah sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight theta space end cell equals cell fraction numerator Panjang space sisi space depan over denominator Panjang space sisi space miring end fraction end cell row blank equals cell fraction numerator 5 square root of 105 space cm over denominator 65 space cm end fraction end cell row blank equals cell fraction numerator square root of 105 over denominator 13 end fraction end cell end table end style  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight theta space end cell equals cell fraction numerator Panjang space sisi space samping over denominator Panjang space sisi space miring end fraction end cell row blank equals cell fraction numerator 40 space cm over denominator 65 space cm end fraction end cell row blank equals cell 8 over 13 end cell end table end style  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Tan space straight theta space end cell equals cell fraction numerator Panjang space sisi space depan over denominator Panjang space sisi space samping end fraction end cell row blank equals cell fraction numerator 5 square root of 105 space cm over denominator 40 space cm end fraction end cell row blank equals cell fraction numerator square root of 105 over denominator 8 end fraction end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos ecan space straight theta space end cell equals cell fraction numerator 1 over denominator sin space straight theta end fraction end cell row blank equals cell fraction numerator 1 over denominator fraction numerator square root of 105 over denominator 13 end fraction end fraction end cell row blank equals cell fraction numerator 13 over denominator square root of 105 end fraction end cell row blank equals cell fraction numerator 13 square root of 105 over denominator 105 end fraction end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell secan space straight theta space end cell equals cell fraction numerator 1 over denominator cos space straight theta end fraction end cell row blank equals cell fraction numerator 1 over denominator 8 over 13 end fraction end cell row blank equals cell 13 over 8 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cotangent space straight theta space end cell equals cell fraction numerator 1 over denominator tan space straight theta end fraction end cell row blank equals cell fraction numerator 1 over denominator fraction numerator square root of 105 over denominator 8 end fraction end fraction end cell row blank equals cell fraction numerator 8 over denominator square root of 105 end fraction end cell row blank equals cell fraction numerator 8 square root of 105 over denominator 105 end fraction end cell end table end style 

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