Question

In △DEF, what is the length of line segment DF?
90

45radical 2

15radical 3

30radical 3

Answer 1

Is there an accompanying picture you could show us? That might help!

Answer 2

yes

Answer 3

Ah, there we go! So it's a triangle with one right angle (90 degrees) and one 30 degree angle. Given that the angles of a triangle add up to 180, the last angle must be 60.

Answer 4

So there's a special way of dealing with 30-60-90 triangles. I am a little rusty, so let me look it up to make sure I've got this.

Answer 5

okay,

Answer 6

did you get the answer

Answer 7

The three sides are always in the ratio 1 to \[\sqrt{3}\] to 2.

So basically the side identified in the drawing is opposite of the 60 degree angle, making it related to the square root of three. The side we're looking for the length of is related to the 2. So

\[45/x = \sqrt{3}/2\]

If you cross-multiply, you get \[90 = x \sqrt{3}\]
Dividing both sides by the square root of three, you get \[90/\sqrt{3}\]
This can be simplified to \[30\sqrt{3}\]

So the last answer is correct.

Answer 8

thank you so much i have a few more you think you could help me out?