Question

In △DEF, what is the length of line segment DF?

Answer 1

You could use the sin function

Answer 2

\[\sin 60 = \frac{27}{DF}\]

Answer 3

Solve for DF and you got it.

Answer 4

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.

Answer 5

\[x ^{2}-x ^{2}/4=27^{2}\]
\[3x^2=2916\]
\[x ^{2}=972\]
\[x \approx31.17\]

Answer 6

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.