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Diketahui segitiga MAB dengan AB equals 300 space cm, sudut MAB equals 60 degree dan sudut ABM equals 75 degree. Maka AM equals ...

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

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Pembahasan

Soal digambarkan sebagai berikut.

Ingatlah bahwa jumlah sudut pada segitiga adalah 180 degree.

Besar sudut M, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell angle AMB end cell equals cell 180 degree minus open parentheses angle MAB plus angle ABM close parentheses end cell row blank equals cell 180 degree minus open parentheses 60 degree plus 75 degree close parentheses end cell row blank equals cell 180 degree minus 135 degree end cell row blank equals cell 45 degree end cell end table

Dengan aturan sinus, diperoleh panjang sisi  AM yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AB over denominator sin space straight M end fraction end cell equals cell fraction numerator AM over denominator sin space straight B end fraction end cell row cell fraction numerator 300 space cm over denominator sin space 45 degree end fraction end cell equals cell fraction numerator AM over denominator sin space 75 degree end fraction end cell row cell fraction numerator 300 space cm over denominator begin display style 1 half square root of 2 end style end fraction end cell equals cell fraction numerator AM over denominator begin display style sin space open parentheses 30 degree plus 45 degree close parentheses end style end fraction end cell row cell 300 space cm times fraction numerator 2 over denominator square root of 2 end fraction end cell equals cell fraction numerator AM over denominator sin space 30 degree times cos space 45 degree plus cos space 30 degree times sin space 45 degree end fraction end cell row cell fraction numerator 600 over denominator square root of 2 end fraction space cm end cell equals cell fraction numerator AM over denominator begin display style 1 half end style times begin display style 1 half end style square root of 2 plus begin display style 1 half end style square root of 3 times begin display style 1 half end style square root of 2 end fraction end cell row cell fraction numerator 600 over denominator square root of 2 end fraction space cm times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell equals cell fraction numerator AM over denominator begin display style 1 fourth end style square root of 2 plus begin display style 1 fourth end style square root of 6 end fraction end cell row cell 600 over 2 square root of 2 space cm end cell equals cell fraction numerator AM over denominator begin display style fraction numerator square root of 2 plus square root of 6 over denominator 4 end fraction end style end fraction end cell row cell 300 square root of 2 space cm end cell equals cell AM times fraction numerator 4 over denominator square root of 2 plus square root of 6 end fraction end cell row cell 4 AM end cell equals cell open parentheses 300 square root of 2 space cm close parentheses open parentheses square root of 2 plus square root of 6 close parentheses end cell row cell 4 AM end cell equals cell 300 square root of 2 times 2 end root plus 300 square root of 2 times 6 end root space cm end cell row cell 4 AM end cell equals cell 300 square root of 4 plus 300 square root of 12 space cm end cell row cell 4 AM end cell equals cell 300 times 2 plus 300 square root of 4 times 3 end root space cm end cell row cell 4 AM end cell equals cell 600 plus 300 times 2 square root of 3 space cm end cell row cell 4 AM end cell equals cell 600 plus 600 square root of 3 space cm end cell row AM equals cell fraction numerator 600 plus 600 square root of 3 space cm end root over denominator 4 end fraction end cell row AM equals cell 150 plus 150 square root of 3 space cm end cell row AM equals cell 409 comma 81 space cm end cell end table

Maka, panjang AM equals 409 comma 81 space cm.

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