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

- anonymous

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

- katieb

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- anonymous

|dw:1360703526596:dw|

- anonymous

Take a look here and see if you can figure it out: See attached

##### 1 Attachment

- Directrix

30-60-90 theorem in words.

##### 1 Attachment

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- anonymous

Thank yoou soo much

- anonymous

@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

- Directrix

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|

- Directrix

Do you understand that so far?

- Directrix

We will go step by step so that you understand. That is why I am asking.

- anonymous

yes

- Directrix

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|

- Directrix

Does that make sense? If so, we're about to break out the theorem. :)

- anonymous

Yes so far.

- Directrix

That's good news. So far, so good.

- Directrix

We want the length of w which is the hypotenuse.
But, all we are given is the 60 leg.

- anonymous

Yes

- Directrix

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.

- Directrix

Theorem Time;
The 60-leg is sqrt(3) times the 30-leg.
Agree?

- anonymous

Whoa, can you draw that??

- Directrix

|dw:1360706227544:dw|

- Directrix

|dw:1360706398553:dw|

- Directrix

Questions? (We have one more step. We are not yet finished.)

- anonymous

I understand

- Directrix

Note that in the latest posted picture, the 60 leg shows up as sqrt(3) times the 30-leg.

- anonymous

Yes, I am aware of that.

- Directrix

The second part of the 30-60-90 theorem states that the hypotenuse is two times the 30-leg.

- Directrix

|dw:1360706596069:dw|

- anonymous

Ok...

- Directrix

So, w = 14. I can write it out.
|dw:1360706716509:dw|

- Directrix

|dw:1360706845397:dw|

- Directrix

You can see the pattern in the diagram. That was what Zelda was talking about.

- Directrix

Question?

- anonymous

No, and Thank You very much.

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