anonymous
  • anonymous
In △DEF, what is the length of line segment DF?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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anonymous
  • anonymous
You could use the sin function
anonymous
  • anonymous
\[\sin 60 = \frac{27}{DF}\]

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anonymous
  • anonymous
Solve for DF and you got it.
Directrix
  • Directrix
DF is the hypotenuse of a 30-60-90 triangle. The 30 leg is EF = 27/√3 = 9√3. DF = twice the 30 leg = 2(9√3) = 18 √3.
mathmagician
  • mathmagician
\[x ^{2}-x ^{2}/4=27^{2}\] \[3x^2=2916\] \[x ^{2}=972\] \[x \approx31.17\]
Directrix
  • Directrix
A 30-60-90 triangle is another example of a special right triangle that has a 30 degree angle and a 60 degree angle. "The hypotenuse and the longer leg in a 30-60-90 triangle can be found when the shorter leg is known. The shorter leg is opposite the 30 angle and the longer leg is opposite the 60 angle" , Here is a theorem that allows you to find the length of the hypotenuse and the longer leg when the length of the shorter leg is known: 30-60-90 Triangle Theorem In a 30-60-90 triangle, the length of the hypotenuse is 2 times the length of the shorter leg and the length of the longer leg is square root 3 times the length of the shorter leg.

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