SOLUTION: In ∆DEF, ∠D is a right angle and m∠F = 30. How long is DF if FE + DE = 12.

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Question 1185236: In ∆DEF, ∠D is a right angle and m∠F = 30. How
long is DF if FE + DE = 12.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Since ∆DEF is a 30-6-90 right triangle

DE%2FFE%22%22=%22%221%2F2

FE%22%22=%22%222%2ADE

FE+%2B+DE%22%22=%22%2212

Substitute 2DE for FE

2%2ADE+%2B+DE%22%22=%22%2212
3%2ADE%22%22=%22%2212
DE%22%22=%22%224

Since ∆DEF is a 30-6-90 right triangle

DF%2FDE%22%22=%22%22sqrt%283%29%2F1

DF%2F4%22%22=%22%22sqrt%283%29%2F1

DF%22%22=%22%224sqrt%283%29

Edwin