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Diketahui kubus ABCD.EFGH dengan AB = 16 cm. Nilai sinus sudut antara garis AH dengan bidang BDHF adalah ....

Diketahui kubus ABCD.EFGH dengan AB = 16 cm. Nilai sinus sudut antara garis AH dengan bidang BDHF adalah ....

  1. begin mathsize 14px style 1 half end style

  2. begin mathsize 14px style 1 third square root of 3 end style

  3. begin mathsize 14px style 1 half square root of 2 end style

  4. begin mathsize 14px style 1 half square root of 3 end style

  5. begin mathsize 14px style 1 third square root of 6 end style

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S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

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Pembahasan

begin mathsize 14px style Dicari space proyeksi space AH space ke space bidang space BDHF comma space yaitu space garis space OH. space  Jadi comma space sudut space yang space terbentuk space adalah space sudut space antara space garis space AH space dan space garis space OH.    AO equals 1 half straight a square root of 2 equals 1 half straight space. straight space 16 square root of 2 equals 8 square root of 2 straight space cm  AH equals straight a square root of 2 equals 16 square root of 2 straight space cm  DO equals 1 half straight a square root of 2 equals 8 square root of 2 straight space cm    OH equals square root of DO squared plus DH squared end root  OH equals square root of open parentheses 8 square root of 2 close parentheses squared plus 16 squared end root  OH equals square root of 128 plus 256 end root  OH equals square root of 384  OH equals 8 square root of 6 straight space cm end style

begin mathsize 14px style cos space invisible function application straight alpha equals fraction numerator open parentheses 16 square root of 2 close parentheses squared plus open parentheses 8 square root of 6 close parentheses squared minus open parentheses 8 square root of 2 close parentheses squared over denominator 2 straight space open parentheses 16 square root of 2 close parentheses open parentheses 8 square root of 6 close parentheses end fraction  cos space invisible function application straight alpha equals fraction numerator 512 plus 384 minus 128 over denominator 512 square root of 3 end fraction  cos space invisible function application straight alpha equals fraction numerator 3 over denominator 2 square root of 3 end fraction equals 1 half square root of 3  straight alpha equals 30 degree    Maka space sin space invisible function application straight alpha equals sin space invisible function application 30 degree equals 1 half end style

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Diketahui kubus ABCD.EFGH mempunyai rusuk = 4 cm . Besar sudut yang dibentuk oleh garis AF dengan bidang ACGE adalah ...

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