How do you find the sides of a triangle if they only give you 1 side but all 3 degrees of the angles.

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- anonymous

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- anonymous

|dw:1336450108160:dw|

- anonymous

That's a special triangle. In the 30-60-90 triangle, the proportion of the sides are \(\ \sqrt{3}:1:2\), respectively.

- anonymous

How would I solve for the sides though?

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- anonymous

So in this case, that means: |dw:1336450392069:dw|

- anonymous

That means the side lengths are ....?

- anonymous

7, 14, and 12?

- anonymous

Use the Law of Sines
http://en.wikipedia.org/wiki/Law_of_sines

- anonymous

Ummm... Well, you have 7, and 14, so substitute 7 as x in the shortest side, and get 7sqrt3.
So the answer is \(\ \huge 7, 14, 7\sqrt{3} \).

- anonymous

I thought that was 7*the sqrt of 3 lol

- anonymous

@robtobey I was going to suggest that at first; however, I think this method is equally as effective.

- anonymous

@ThaJokersRiddles Does this make sense to you now?

- anonymous

Yea

- anonymous

The problem statement does not infer a right triangle.

- anonymous

Great!

- anonymous

@robtobey, @ThaJokersRiddles drew the problem that indicates a right angle.

- anonymous

Ok. I stand corrected.

- anonymous

However, the law of sines would be effective had this been a non-right triangle.

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