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Diketahui rusuk kubus ABCD.EFGH adalah a satuan, tangen sudut antara garis AH dan bidang BDHF adalah ....

  1. begin mathsize 14px style 1 third end style

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

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

  4. 1

  5. begin mathsize 14px style square root of 3 end style

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style Dicari space proyeksi space AH space ke space bidang space BDHF comma space yaitu space garis space OH.  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  AH equals straight a square root of 2  DO equals 1 half straight a square root of 2    OH equals square root of OD squared plus DH squared end root  OH equals square root of open parentheses 1 half straight a square root of 2 close parentheses squared plus straight a squared end root  OH equals square root of 6 over 4 straight a squared end root  OH equals 1 half straight a square root of 6 end style

begin mathsize 14px style cos invisible function application space straight alpha equals fraction numerator open parentheses straight a square root of 2 close parentheses squared plus open parentheses 1 half straight a square root of 6 close parentheses squared minus open parentheses 1 half straight a square root of 2 close parentheses squared over denominator 2 straight space open parentheses straight a square root of 2 close parentheses open parentheses 1 half straight a square root of 6 close parentheses end fraction  cos space invisible function application straight alpha equals fraction numerator 3 straight a squared over denominator 2 straight a squared square root of 3 end fraction equals 1 half square root of 3  straight alpha equals 30 degree  Maka comma space tan space invisible function application straight alpha equals tan space invisible function application 30 degree equals 1 third square root of 3 end style

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