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If △DEF is a 30-60-90 triangle with m∠F = 90°, m∠E = 60°, and FE = 16, find the EXACT value of DE.

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f △DEF is a 30-60-90 triangle with m∠F = 90°, m∠E = 60°, and FE = 16, find the EXACT value of DF.

 Apr 27, 2020
 #1
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Tan 60 =  sin 60 / cos 60 = sqrt3/2  / 1/2 = sqrt 3

 

16  tan 60 = DF  =   16 sqrt 3

 

sin 60 = sqrt 3 / 2   = DF/DE

              sqrt3 /2 =   16 sqrt3 / DE

 

               DE = 16 sqrt3 / (sqrt3 /2) = 32

 Apr 27, 2020

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