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

 

 Feb 13, 2021
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BD  =  sart [ BC^2  +  BD^2  ]  =sqrt  [ (sqrt 3)^2  + 2^2  ] =   sqrt  [ 3 + 4 ]  =  sqrt  [7]

 

sin BDC   = BC / BD  =  sqrt (3) / sqrt (7)

 

Using  the Law of Sines

 

EC  / sin BDC  = DC  /sin  90

 

EC  / (sqrt (3)  / sqrt (7))  = 2  /1

 

EC  =  2sqrt (3)   / sqrt (7)  =  2sqrt (21) / 7

 

 

cool cool cool

 Feb 14, 2021

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