Question

In △DEF, what is the length of DF?

Answer 1

I know that it is smaller than DE + EF, but that's about it.

Answer 2

Ah, a 30-60-90 triangle. Do you know the ratios of this special triangle, or do you know any basic trigonometry?

Answer 3

not at all :/

Answer 4

Alright, well, this is one of those situations where you just have to know certain facts.

Answer 5

Those are the ratios of side lengths for a 30-60-90 triangle.
The 27 is across from the 60º angle so it is in the ratio of x√3

Answer 6

so the equation
would be x squared plus27 squared equals 2xsquared

Answer 7

You can use that, yes. Pythagorean theorem is always applicable to right triangles.

Answer 8

andthen what

Answer 9

You are looking for 2x, though, and you know that 27=x√3, so you can solve
\[\large x\sqrt{3}=27\]
for x and then double it to find 2x = DF.

Answer 10

so 54?

Answer 11

How did you get 54?