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Jika diketahui segitiga ABC, dengan ukuran panjang sisi b = 20 , besar ∠ C = 10 5 ∘ dan besar ∠ B = 4 5 ∘ . Hitungpanjang sisi a dan c !

Jika diketahui segitiga ABC, dengan ukuran panjang sisi , besar  dan besar . Hitung panjang sisi  dan !

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F. Ayudhita

Master Teacher

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Mencari sudut : Dengan aturan sinus,panjang sisi : Dengan aturan cosinus, panjang sisi : Dengan rumus kuadratik: Karena besar , maka panjang sisi

Mencari sudut begin mathsize 14px style A end style :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell angle A end cell equals cell 180 to the power of ring operator minus angle B minus angle C end cell row blank equals cell 180 to the power of ring operator minus 45 to the power of ring operator minus 105 to the power of ring operator end cell row blank equals cell 30 to the power of ring operator end cell end table end style

Dengan aturan sinus, panjang sisi begin mathsize 14px style a end style :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a over denominator sin space A end fraction end cell equals cell fraction numerator b over denominator sin space B end fraction end cell row cell fraction numerator a over denominator sin space 30 to the power of ring operator end fraction end cell equals cell fraction numerator 20 over denominator sin space 45 to the power of ring operator end fraction end cell row a equals cell fraction numerator 20 over denominator begin display style 1 half end style square root of 2 end fraction cross times 1 half end cell row a equals cell 10 square root of 2 end cell end table end style

Dengan aturan cosinus, panjang sisi begin mathsize 14px style c end style :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a squared end cell equals cell b squared plus c squared minus 2 b c times cos space A end cell row cell left parenthesis 10 square root of 2 right parenthesis squared end cell equals cell 20 to the power of 2 end exponent plus c squared minus 2 times left parenthesis 20 right parenthesis times c times 1 half square root of 3 end cell row 200 equals cell 400 plus c squared minus 20 square root of 3 c end cell row 0 equals cell c squared minus 20 square root of 3 c plus 200 end cell end table end style

Dengan rumus kuadratik :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell c subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative left parenthesis negative 20 square root of 3 right parenthesis plus-or-minus square root of open parentheses 20 square root of 3 close parentheses squared minus 4 times 1 times 200 end root over denominator 2 times 1 end fraction end cell row blank equals cell fraction numerator 20 square root of 3 plus-or-minus 20 over denominator 2 end fraction end cell row blank equals cell 10 square root of 3 plus-or-minus 10 end cell end table end style

Karena besar begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank angle end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table table attributes columnalign right center left columnspacing 0px end attributes row blank greater than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank angle end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank B end table table attributes columnalign right center left columnspacing 0px end attributes row blank greater than blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank angle end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank A end table end style, maka panjang sisi undefined

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