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ABCD adalah empat persegi panjang pada bidang hori...

ABCD adalah empat persegi panjang pada bidang horisontal, dan ADEF empat persegi panjang pula pada bidang vertikal. Panjang AF= 3 m, BC= 4 m dan CE = 7 m. Jika a dan ~ berturut-turut sudut anfara BE dengan bidang ABCD dan bidarig ADEF maka tan a tan b adalah .....

  1. fraction numerator 3 over denominator square root of 35 end fraction

  2. fraction numerator 3 over denominator square root of 35 end fraction

  3. fraction numerator 5 over denominator square root of 35 end fraction

  4. fraction numerator 4 over denominator square root of 21 end fraction

  5. fraction numerator 5 over denominator square root of 21 end fraction

Jawaban:

Keterangan :

A F equals space 3 space m space  C E equals space 7 space m space  B C equals space 4 space m  A B space equals C D  C D equals square root of C E squared minus A F squared end root  C D equals square root of 72 minus 32 end root  C D equals square root of 49 minus 9 end root  C D equals square root of 40    B D equals square root of C D squared plus B C squared end root  B D equals square root of left parenthesis square root of 40 right parenthesis squared plus 4 squared end root  B D equals square root of 40 plus 16 end root  B D equals square root of 56    tan equals fraction numerator D E over denominator B D end fraction equals fraction numerator 3 over denominator square root of 56 end fraction  E A equals square root of D E squared plus A D squared end root  E A equals square root of 3 squared plus 4 squared end root  E A equals square root of 9 plus 16 end root  E A equals square root of 25  E A equals 5  left parenthesis tan space alpha right parenthesis left parenthesis tan space beta right parenthesis equals open parentheses fraction numerator 3 over denominator square root of 56 end fraction close parentheses open parentheses fraction numerator square root of 56 over denominator 5 end fraction close parentheses equals fraction numerator 3 over denominator square root of 35 end fraction

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