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Perhatikan gambar segitiga ABC di bawah ini. Diketahui dan . Tentukan panjang BC.

Perhatikan gambar segitiga ABC di bawah ini. Diketahui begin mathsize 14px style text ∠ABC=90°, ∠CDB=45°, ∠CAB=30° end text end style dan begin mathsize 14px style text AD=2 cm end text end style. Tentukan panjang BC.

 

Jawaban:

Lihat begin mathsize 14px style triangle BDC comma space angle CDB equals 45 degree comma angle straight B equals 90 degree comma space maka space angle DCB equals 45 degree end style.

Jadi begin mathsize 14px style triangle BDC end style adalah segitiga siku-siku sama kaki.

Misal: Panjang DB adalah x, maka

undefined  undefined undefined 
DB BC DC
x x begin mathsize 14px style x square root of 2 end style 

Lihat begin mathsize 14px style triangle ABC space end style 

begin mathsize 14px style 30 degree end style begin mathsize 14px style 60 degree end style  undefined 
BC AB AC
x 2+x 2x

Lihat begin mathsize 14px style triangle ABC comma space siku minus siku end style berlaku teorema Pythagoras

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight x squared plus open parentheses 2 plus straight x close parentheses squared end cell equals cell open parentheses 2 straight x close parentheses squared end cell row cell straight x squared plus 4 plus 4 straight x plus straight x squared end cell equals cell 4 straight x squared end cell row 0 equals cell 2 straight x squared minus 4 straight x minus 4 end cell row 0 equals cell straight x squared minus 2 straight x minus 2 end cell row cell straight x subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative open parentheses negative 2 close parentheses plus-or-minus square root of open parentheses negative 2 close parentheses squared minus 4 open parentheses 1 close parentheses open parentheses negative 2 close parentheses end root over denominator 2 open parentheses 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 plus-or-minus square root of 4 plus 8 end root over denominator 2 end fraction end cell row blank equals cell fraction numerator 2 plus-or-minus 2 square root of 3 over denominator 2 end fraction end cell row blank equals cell 1 plus-or-minus square root of 3 end cell row blank blank blank end table end style 

Karena panjang sisi tidak mungkin negatif, kita ambil yang positif yaitu begin mathsize 14px style x equals 1 plus square root of 3 end style.

Jadi, panjang BC adalah begin mathsize 14px style 1 plus square root of 3 end style cm.

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