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Dalam segitiga ABC, siku-siku di A diketahui panjang BC = a, (adalah bilangan positif) dan cos ∠ABC=22​​  . Tentukan panjang garis tinggi AD.

Pertanyaan

Dalam segitiga ABC, siku-siku di  diketahui panjang  = ,

(adalah bilangan positif) dan begin mathsize 14px style cos space angle A B C equals fraction numerator square root of 2 over denominator 2 end fraction space end style . Tentukan panjang garis tinggi AD.

 

R. Trihandayani

Master Teacher

Jawaban terverifikasi

Pembahasan

perhatikan gambar pada soal.

Diketahui bahwa begin mathsize 14px style B C equals a end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space angle A B C end cell equals cell fraction numerator square root of 2 over denominator 2 end fraction end cell row cell fraction numerator A B over denominator B C end fraction end cell equals cell fraction numerator square root of 2 over denominator 2 end fraction end cell row cell fraction numerator A B over denominator a end fraction end cell equals cell fraction numerator square root of 2 over denominator 2 end fraction end cell row cell A B end cell equals cell fraction numerator a square root of 2 over denominator 2 end fraction end cell end table end style 

dengan menggunakan rumus Pythagoras

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A C end cell equals cell square root of B C squared minus A B squared end root end cell row blank equals cell square root of a squared minus open parentheses fraction numerator a square root of 2 over denominator 2 end fraction close parentheses squared end root end cell row blank equals cell square root of a squared minus fraction numerator 2 a squared over denominator 4 end fraction end root end cell row blank equals cell square root of fraction numerator 4 a squared minus 2 a squared over denominator 4 end fraction end root end cell row blank equals cell square root of fraction numerator 2 a squared over denominator 4 end fraction end root end cell row blank equals cell a over 2 square root of 2 end cell end table end style 

dengan menggunakan perbandingan segitiga maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell L subscript 1 end cell equals cell L subscript 2 end cell row cell 1 half times A D times B C end cell equals cell 1 half times A B times A C end cell row cell 1 half times A D times a end cell equals cell 1 half times fraction numerator a square root of 2 over denominator 2 end fraction times fraction numerator a square root of 2 over denominator 2 end fraction end cell row cell A D end cell equals cell 1 half a end cell row blank blank blank end table end style 

maka nilai begin mathsize 14px style A D equals 1 half a end style.  

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