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 .....

$fraction numerator 3 over denominator square root of 35 end fraction$
$fraction numerator 3 over denominator square root of 35 end fraction$
$fraction numerator 5 over denominator square root of 35 end fraction$
$fraction numerator 4 over denominator square root of 21 end fraction$
$fraction numerator 5 over denominator square root of 21 end fraction$

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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