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Diketahui kubus KLMN.PQRS dengan panjang rusuk . N...

Diketahui kubus KLMN.PQRS dengan panjang rusuk 6 space cm. Nilai sinus antara garis LS dengan Bidang PQRS adalah ...

Jawaban:

Perhatikan gambar berikut:



SQ adalah diagonal bidang kubus, dengan menggunakan teorema Pythagoras maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row SQ equals cell square root of PS squared plus PQ squared end root end cell row blank equals cell square root of 6 squared plus 6 squared end root end cell row blank equals cell square root of 36 plus 36 end root end cell row blank equals cell square root of 36 cross times 2 end root end cell row blank equals cell 6 square root of 2 space cm end cell end table 

dan LS adalah diagonal ruang kubus maka:

table attributes columnalign right center left columnspacing 0px end attributes row LS equals cell square root of PQ squared plus LQ squared end root end cell row blank equals cell square root of open parentheses 6 square root of 2 close parentheses squared plus 6 squared end root end cell row blank equals cell square root of 72 plus 36 end root end cell row blank equals cell square root of 108 end cell row blank equals cell square root of 36 cross times 3 end root end cell row blank equals cell 6 square root of 3 space cm end cell end table

Ingat definisi sinus maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight alpha end cell equals cell fraction numerator sisi space depan over denominator sisi space miring end fraction end cell row blank equals cell LQ over LS end cell row blank equals cell fraction numerator 6 over denominator 6 square root of 3 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell 1 third square root of 3 end cell end table 

Dengan demikian nilai sinus antara garis LS dengan Bidang PQRS adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 3 end cell end table.

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