## ThaJokersRiddles 3 years ago 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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1. ThaJokersRiddles

|dw:1336450108160:dw|

2. Study23

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

3. ThaJokersRiddles

How would I solve for the sides though?

4. Study23

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

5. Study23

That means the side lengths are ....?

6. ThaJokersRiddles

7, 14, and 12?

7. robtobey

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

8. Study23

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

9. ThaJokersRiddles

I thought that was 7*the sqrt of 3 lol

10. Study23

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

11. Study23

@ThaJokersRiddles Does this make sense to you now?

12. ThaJokersRiddles

Yea

13. robtobey

The problem statement does not infer a right triangle.

14. Study23

Great!

15. Study23

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

16. robtobey

Ok. I stand corrected.

17. Study23

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