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What is the value of w? triangle (1 point) 7 3.5 7square root of three 14

Mathematics
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|dw:1360703526596:dw|
Take a look here and see if you can figure it out: See attached
30-60-90 theorem in words.
1 Attachment

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Other answers:

Thank yoou soo much
@Directrix I'm sorry I thought I understood what I was doing but if you could just explain how to solve for w please, and @Zelda if you can help i would appreciate it
First, you have to know what the 30-60-90 theorem says. It is written above in both symbols and words. Next, you have to know the names of the parts of the 30-60-90 triangle. I am marking them on a drawing. |dw:1360705600824:dw|
Do you understand that so far?
We will go step by step so that you understand. That is why I am asking.
yes
If one angle of a right triangle is 30, then the other acute angle is 60. So, we have a 60 leg. Then, there is the hypotenuse. |dw:1360705782032:dw|
Does that make sense? If so, we're about to break out the theorem. :)
Yes so far.
That's good news. So far, so good.
We want the length of w which is the hypotenuse. But, all we are given is the 60 leg.
Yes
When fooling with the 30-60-90 theorem, get the 30-leg first. I know we are not asked for the 30-leg but the 30-leg is the key to finding w, the hypotenuse.
Theorem Time; The 60-leg is sqrt(3) times the 30-leg. Agree?
Whoa, can you draw that??
|dw:1360706227544:dw|
|dw:1360706398553:dw|
Questions? (We have one more step. We are not yet finished.)
I understand
Note that in the latest posted picture, the 60 leg shows up as sqrt(3) times the 30-leg.
Yes, I am aware of that.
The second part of the 30-60-90 theorem states that the hypotenuse is two times the 30-leg.
|dw:1360706596069:dw|
Ok...
So, w = 14. I can write it out. |dw:1360706716509:dw|
|dw:1360706845397:dw|
You can see the pattern in the diagram. That was what Zelda was talking about.
Question?
No, and Thank You very much.

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