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Pertanyaan

Pada segi empat ABCD berikut, ∠ ADB = α .Tentukan nilai cos α .

Pada segi empat  berikut,  .  Tentukan nilai  

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F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai

nilai begin mathsize 14px style cos space alpha equals 1 fifth square root of 17 end style

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Pembahasan

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Mencari panjang BD Mencari panjang AD Mencari nilai Jadi nilai

Mencari panjang BD

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell B D end cell equals cell square root of B C squared plus C D squared end root end cell row blank equals cell square root of open parentheses 3 square root of 2 close parentheses squared plus open parentheses square root of 7 close parentheses squared end root end cell row blank equals cell square root of 18 plus 7 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table end style

Mencari panjang AD

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell A D end cell equals cell square root of B D squared minus A B squared end root end cell row blank equals cell square root of 5 squared minus open parentheses 2 square root of 2 close parentheses squared end root end cell row blank equals cell square root of 25 minus 8 end root end cell row blank equals cell square root of 17 end cell end table end style

Mencari nilai begin mathsize 14px style cos space alpha end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator A D over denominator B D end fraction end cell row blank equals cell fraction numerator square root of 17 over denominator 5 end fraction end cell row blank equals cell 1 fifth square root of 17 end cell end table end style

Jadi nilai begin mathsize 14px style cos space alpha equals 1 fifth square root of 17 end style

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