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In rectangle ABCD, shown here, CE is perpendicular to BD . If BC = sqrt(3) and DC = 2, what is CE?

 

 Aug 3, 2021
 #1
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Angle  EDC = arctan (sqrt(3)/2) = 40.9 degrees

   then angle ECD  = 180 - 90 - 40.9 =  49.1 degrees

     cos (ECD) = adj / hyp 

     cos (49.1) = EC / 2

         EC = 1.3 units

 Aug 3, 2021
 #2
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BD = √7

 

[ABCD] = 2√3

 

CE = [ABCD] / √7

 Aug 4, 2021

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