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Luas segitiga siku-siku RST , dengan sisi tegak RS adalah 20 c m 2 . Tentukan nilai sinus, cosinus, dan tangen untuk sudut lancip T

Luas segitiga siku-siku $RST$ , dengan sisi tegak $RS$ adalah $20 c m^{2}$ . Tentukan nilai sinus, cosinus, dan tangen untuk sudut lancip T

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Pembahasan

perhatikan gambar segitiga berikut ini. Diketahui bahwa luas segitiga adalah , maka dengan menggunakan Phytagoras maka nilai dari sudut T

perhatikan gambar segitiga berikut ini.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space T end cell equals cell fraction numerator d e over denominator m i end fraction end cell row cell cos space T end cell equals cell fraction numerator s a over denominator m i end fraction end cell row cell tan space T end cell equals cell fraction numerator d e over denominator s a end fraction end cell end table end style$

Diketahui bahwa luas segitiga adalah , maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row L equals cell 1 half times x times t end cell row 20 equals cell 1 half times x times t end cell row t equals cell 40 over x end cell end table end style

dengan menggunakan Phytagoras

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S T end cell equals cell square root of R S squared plus R T squared end root end cell row blank equals cell square root of x squared plus t squared end root end cell row blank equals cell square root of x squared plus open parentheses 40 over x close parentheses squared end root end cell row blank equals cell square root of x squared plus 1600 over x squared end root end cell row blank equals cell square root of fraction numerator x to the power of 4 plus 1600 over denominator x squared end fraction end root end cell row blank equals cell fraction numerator square root of x to the power of 4 plus 1600 end root over denominator x end fraction end cell end table end style$

maka nilai dari sudut T

$begin mathsize 14px style sin space T equals fraction numerator R S over denominator S T end fraction end style$
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space T end cell equals cell fraction numerator open parentheses begin display style 40 over x end style close parentheses over denominator open parentheses begin display style fraction numerator square root of x to the power of 4 plus 1600 end root over denominator x end fraction end style close parentheses end fraction end cell row blank equals cell fraction numerator 40 over denominator square root of x to the power of 4 plus 1600 end root end fraction times fraction numerator square root of x to the power of 4 plus 1600 end root over denominator square root of x to the power of 4 plus 1600 end root end fraction end cell row blank equals cell fraction numerator 40 over denominator x to the power of 4 plus 1600 end fraction square root of x to the power of 4 plus 1600 end root end cell end table end style$
$begin mathsize 14px style cos space T equals fraction numerator R T over denominator S T end fraction end style$
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space T end cell equals cell fraction numerator x over denominator open parentheses begin display style fraction numerator square root of x to the power of 4 plus 1600 end root over denominator x end fraction end style close parentheses end fraction end cell row blank equals cell fraction numerator x squared over denominator square root of x to the power of 4 plus 1600 end root end fraction times fraction numerator square root of x to the power of 4 plus 1600 end root over denominator square root of x to the power of 4 plus 1600 end root end fraction end cell row blank equals cell fraction numerator x squared over denominator x to the power of 4 plus 1600 end fraction square root of x to the power of 4 plus 1600 end root end cell end table end style$
$begin mathsize 14px style tan space T equals fraction numerator R S over denominator R T end fraction end style$
$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space T end cell equals cell fraction numerator open parentheses begin display style 40 over x end style close parentheses over denominator x end fraction end cell row blank equals cell 40 over x squared end cell end table end style$