# Thread: Length of triangle problem?

1. ## Length of triangle problem?

Hi, this is my first time here. I'm sorry if I am posting this in the wrong place, as I wasn't quite sure where I should put this question. So if it is in the wrong place, I apologize.

Any who, I need to find the length of side "AC" for the smaller square. I made a picture of what the square looks like here.

2. Originally Posted by steventhedog
Hi, this is my first time here. I'm sorry if I am posting this in the wrong place, as I wasn't quite sure where I should put this question. So if it is in the wrong place, I apologize.

Any who, I need to find the length of side "AC" for the smaller square. I made a picture of what the square looks like here.
The Geometry forum might be a better place, but I see nothing terribly wrong with putting it here. If one of the mods disagrees, they'll probably just move it.

There's a problem with your triangle. I'll show you when it comes up.

You have two approaches you can use, either the Law of Sines or the Law of Cosines. No matter what you do you will have to find one of the other angles in the triangle. It looks to me that you can only directly find angle C (then 180 - C - 62 = B). So let's find angle C using the Law of Sines:
sin(62)/9 = sin(C)/12

sin(C) = (12/9)*sin(62) = 1.17726

BUT sin(C) must be less than or equal to 1. Thus this triangle cannot exist. Was there a typo of some sort?

-Dan

3. Hmmm, no I am pretty sure there is no typo. However I suppose the original problem could have had a typo, that could be why I was running into trouble with it. I'll take a look and get back to ya.

4. Hello, steventhedog!

I need to find the length of side "AC" for the smaller square. . Square?
Sorry, but that makes me mistrust anything you say.

What is the purpose of the first triangle?
. . It too is an impossible triangle.
The sine of angle T turns out to be greater than 1
. . which not possible.

5. oops, just looked at the question again, I figured out the answer. Turns out I was looking at the wrong triangle and wrong question. lol. Sorry for the inconvenience, thanks for your help though.