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.
+129907
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
+1641 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.
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sin(B) = 8 / 17 = 0.470588235
sin(C) = 15 / 17 = 0.882352941
(x / sinB) + (x / sinC) = 17 ==> x = 5.217391
