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Perhatikan gambar di bawah.  Jika   maka panjang ...

Perhatikan gambar di bawah. 

Jika angle BAC equals angle BED equals angle ABD equals 90 degree comma EC equals 2 straight a comma space EB equals straight a space dan space AB equals straight b maka panjang DE adalah...

  1. fraction numerator a plus b over denominator square root of 9 a squared minus b squared end root end fraction 

  2. fraction numerator b over denominator square root of 9 a squared minus b squared end root end fraction

  3. fraction numerator a b over denominator square root of 9 a squared minus b squared end root end fraction 

  4. fraction numerator 2 a b over denominator square root of 9 a squared minus b squared end root end fraction 

  5. fraction numerator a b over denominator square root of 9 a squared minus b squared end root end fraction 

Jawaban:

Misalkan angle ABC equals x dan angle EBD equals y.

Karena angle ABD siku-siku, maka table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y end cell equals cell 90 degree end cell end table. Sehingga table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 90 degree minus x end cell end table atau  table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 90 degree minus y end cell end table.

Besar angle ACB

table attributes columnalign right center left columnspacing 0px end attributes row cell angle ACB end cell equals cell 180 degree minus 90 degree minus x end cell row blank equals cell 90 degree minus x end cell row blank equals y end table 

Besar angle EDB

table attributes columnalign right center left columnspacing 0px end attributes row cell angle EDB end cell equals cell 180 degree minus 90 degree minus y end cell row blank equals cell 90 degree minus y end cell row blank equals x end table 

Panjang sisi AC 

table attributes columnalign right center left columnspacing 0px end attributes row AC equals cell square root of BC squared minus AB squared end root end cell row blank equals cell square root of left parenthesis 3 a right parenthesis squared minus b to the power of 2 end exponent end root end cell row blank equals cell square root of 9 a squared minus b squared end root end cell end table 

Perhatikan segitiga ABC.

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space angle ACB end cell equals cell tan space y end cell row blank equals cell AB over AC end cell row blank equals cell fraction numerator b over denominator square root of 9 a squared minus b squared end root end fraction end cell end table 

Perhatikan segitiga BDE.

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space angle EBD end cell equals cell tan space y end cell row blank equals cell DE over BE end cell row blank equals cell DE over a end cell end table 

Diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space y end cell equals cell tan space y end cell row cell fraction numerator b over denominator square root of 9 a squared minus b squared end root end fraction end cell equals cell DE over a end cell row cell fraction numerator b over denominator square root of 9 a squared minus b squared end root end fraction times a end cell equals DE row cell fraction numerator a b over denominator square root of 9 a squared minus b squared end root end fraction end cell equals DE row blank blank blank end table 

Jadi, jawaban yang benar adalah E. 

 

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