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In right triangle ABC, AC = 8, AB = 15, and BC = 17.  Square ADEF is inscribed in the square.  Find the side length of square ADEF.

 

 Dec 15, 2020
 #1
avatar+114221 
+1

 

Note that triangle EFB  is similar to triangle CAB

 

So  

 

CA/ CB   =  EF / EB

 

8/17  = x/ EB

 

EB =  (17/8)x

 

And

 

Triangle  CDE is also similar to triangle CAB

 

So

 

DE/CE =  AB/ CB

 

x / CE  = 15/17

 

CE  = (15/17) x

 

And 

 

CB  = CE  + EB

 

17 =  ( 17/8)x + (15/17)x

 

17  = (409/136)  x

 

17(136/409)  =  x  = 2312/409 ≈   5.653

 

 

cool cool cool

 Dec 15, 2020
 #3
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0

Let's check your answer quickly:

 

5.653 + (5.653 / tan(B)) = 16.252375

 

Please correct your answer!

Thanks!

Guest Dec 15, 2020
 #2
avatar+846 
+3

In right triangle ABC, AC = 8, AB = 15, and BC = 17.  Square ADEF is inscribed in the square.  Find the side length of square ADEF.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

sin(B) = 8 / 17 = 0.470588235

 

sin(C) = 15 / 17 = 0.882352941

 

(x / sinB) + (x / sinC) = 17     ==>  x = 5.217391

 Dec 15, 2020

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