SOLUTION: Given: right △DEF with m∠E = 2 · m∠F and EF = 14 radical 3 Find: DE and DF in simplest radical form and approximation

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Question 1193781: Given: right △DEF with
m∠E = 2 · m∠F
and EF = 14 radical 3
Find: DE and DF in simplest radical form and approximation
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The description is a 30-60-90 Right Triangle, EF=14sqrt%283%29, and DE=%281%2F2%2914sqrt%283%29 or 7sqrt%283%29.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
Given: right △DEF with
m∠E = 2 · m∠F
and EF = 14 radical 3
Find: DE and DF in simplest radical form and approximation 
2 scenarios exist. 

1) ∡s E, D, and F can be 90o, 45o, and 45o, respectively.

2) ∡s E, D, and F can ALSO be 60o, 90o, and 30o, respectively.

This triangle can therefore be a 45-45-90 special triangle, or one of the 30-60-90 variety, since DE and DF can EACH have 2 different lengths.