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Diketahui kubus PQRS.TUVW dengan panjang rusuk 5 cm. Jika beta merupakan sudut antara bidang PWR dan bidang PRS, maka cos beta...

  1. 1 third square root of 7

  2. 1 third square root of 6

  3. 1 third square root of 5

  4. 2 over 3

  5. 1 third square root of 3

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

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Pembahasan

Sudut antara bidang PWR dengan PRS adalah angle W Q S equals beta

*SW=5 cm

asterisk times Q S equals a square root of 2 equals 5 square root of 2 space c m  asterisk times S A equals 1 half Q S equals 5 over 2 square root of 2  asterisk times W A equals square root of S W squared plus S A squared end root  space space space space space space space space equals square root of 5 squared plus open parentheses 5 over 2 square root of 2 close parentheses squared end root  space space space space space space space space equals square root of 25 plus 25 over 2 end root equals square root of 75 over 2 end root equals square root of fraction numerator 25 x 3 over denominator 2 end fraction end root  space space space space space space space space equals 5 fraction numerator square root of 3 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals fraction numerator 5 square root of 6 over denominator 2 end fraction  asterisk times cos beta equals fraction numerator S A over denominator W A end fraction equals fraction numerator begin display style 5 over 2 end style square root of 2 over denominator begin display style 5 over 2 end style square root of 6 end fraction equals fraction numerator square root of 2 over denominator square root of 6 end fraction cross times fraction numerator square root of 6 over denominator square root of 6 end fraction equals fraction numerator square root of 12 over denominator 6 end fraction  space space space space space space space space space space space equals fraction numerator 2 square root of 3 over denominator 6 end fraction equals 1 third square root of 3

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