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https://latex.artofproblemsolving.com/0/9/0/090ba6228af39380edfafa9908b8a3dd14b7a383.png

 Apr 5, 2019
edited by notsmart2.0  Apr 5, 2019
 #1
avatar+99237 
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Can't tell what the letter at the top left of the figure is...but...I think it is "H"

 

Anyway....join  H and Y 

 

Triangle HAY   is a isoceles right triangle.....with HX = XY

So....

HY =  sqrt [ HX^2 + XY^2]  =  sqrt [ 4^2 + 4^2 ] =  sqrt [ 32]   

 

And......HY will create  triangle HYZ

Angle HYX =  135 - Angle  HYX

Angle HYX = 135 - 45  = 90

 

So....triangle HYZ is right wth HZ the hypotenuse  and HY one of the legs

 

So

 

"a"  = ZY  =  sqrt [ HZ^2 - HY^2]  =  sqrt [ 9^2 - 32]  = sqrt [ 81 - 32] = sqrt  [49]  =  7

 

 

cool cool cool

 Apr 5, 2019

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