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# can i get a hint

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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

### 3+0 Answers

#1
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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   Dec 15, 2020
#3
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Let's check your answer quickly:

5.653 + (5.653 / tan(B)) = 16.252375

Please correct your answer!

Thanks!

Guest Dec 15, 2020
#2
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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.

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

sin(B) = 8 / 17 = 0.470588235

sin(C) = 15 / 17 = 0.882352941

(x / sinB) + (x / sinC) = 17     ==>  x = 5.217391 Dec 15, 2020