document.write( "Question 1193782: Given: right △DEF with m∠F = 30° and
\n" ); document.write( "FE = 18
\n" ); document.write( "Find: DF and DE in simplest radical form and approximation. \n" ); document.write( "
Algebra.Com's Answer #825818 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "Given: right △DEF with m∠F = 30° and
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\n" ); document.write( "Find: DF and DE in simplest radical form and approximation.
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\n" ); document.write( "\n" ); document.write( "As worded,  printed,  posted and presented,  the problem is posed  INCORRECTLY.\r
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\n" ); document.write( "\n" ); document.write( "To be posed correctly,  it must specify if  FE  is the leg or it is the hypotenuse.\r
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\n" ); document.write( "\n" ); document.write( "Or,  alternatively,  it must say which angle is right angle.\r
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\n" ); document.write( "\n" ); document.write( "comment from student :   Angle  D  is the right angle.\r
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\n" ); document.write( "\n" ); document.write( "My response :   if so,  then  FE  is the hypotenuse,  angle  F  is  30°,  and  DE  is the leg opposite to angle of  30°.\r
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\n" ); document.write( "\n" ); document.write( "In such right angled triangle,  the leg opposite to the angle of  30°  is half the hypotenuse.\r
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\n" ); document.write( "\n" ); document.write( "So,  DE = 18/2 = 9 units.\r
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\n" ); document.write( "\n" ); document.write( "Leg   DF   is then   \"sqrt%28FE%5E2+-+DE%5E2%29\" = \"sqrt%2818%5E2+-+9%5E2%29\" = \"sqrt%28243%29\" = \"sqrt%2881%2A3%29\" = \"9%2Asqrt%283%29\".\r
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\n" ); document.write( "\n" ); document.write( "ANSWER.   DE = 9;   DF = \"9sqrt%283%29\" = 15.59   (rounded).\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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