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Diketahui kubus ABCD.EFGH dengan panjang rusuk 6 cm. Nilai sin ∠ (BDE,BDG) adalah ...

Diketahui kubus ABCD.EFGH dengan panjang rusuk 6 cm. Nilai sin (BDE,BDG) adalah ...

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Jawaban terverifikasi

Jawaban

Nilai sin (BDE,BDG) adalah .

 Nilai sin begin mathsize 14px style angle end style(BDE,BDG) adalah begin mathsize 14px style fraction numerator 2 square root of 2 over denominator 3 end fraction end style.

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Perhatikan gambar! (BDE,BDG) = EOG EO = GO EG = AC = diagonal bidang = Jadi,Nilai sin (BDE,BDG) adalah .

Perhatikan gambar!

begin mathsize 14px style angle end style(BDE,BDG) = begin mathsize 14px style angle end styleEOG

EO = GO

EG = AC = diagonal bidang = begin mathsize 14px style 6 square root of 2 end style

table attributes columnalign right center left columnspacing 0px end attributes row cell E O squared end cell equals cell E A squared plus A O squared end cell row blank equals cell 6 squared plus left parenthesis 3 square root of 2 right parenthesis squared end cell row blank equals cell 36 plus 18 end cell row blank equals 54 row blank blank blank row cell E O end cell equals cell plus-or-minus square root of 54 end cell row blank equals cell plus-or-minus 3 square root of 6 end cell row blank equals cell 3 square root of 6 end cell row blank blank blank end table

table attributes columnalign right center left columnspacing 0px end attributes row cell E G squared end cell equals cell E O squared plus O G squared minus 2 cross times E O cross times O G space cos space E O G end cell row cell open parentheses 6 square root of 2 close parentheses squared end cell equals cell open parentheses 3 square root of 6 close parentheses squared plus open parentheses 3 square root of 6 close parentheses squared minus 2 open parentheses 3 square root of 6 close parentheses open parentheses 3 square root of 6 close parentheses space cos space E O G end cell row 72 equals cell 54 plus 54 minus 108 space cos space E O G end cell row cell 108 space cos space E O G end cell equals 36 row cell cos space E O G end cell equals cell 36 over 108 end cell row cell cos space E O G end cell equals cell 1 third end cell row cell 1 third end cell equals cell samping over miring end cell row depan equals cell square root of 3 squared minus 1 squared end root end cell row blank equals cell square root of 9 minus 1 end root end cell row blank equals cell square root of 8 end cell row blank equals cell 2 square root of 2 end cell row cell sin space alpha end cell equals cell depan over miring end cell row blank equals cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell row blank blank space row blank blank blank end table

Jadi, Nilai sin begin mathsize 14px style angle end style(BDE,BDG) adalah begin mathsize 14px style fraction numerator 2 square root of 2 over denominator 3 end fraction end style.

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