Solving right triangle

I am in need of help solving this problem. I got the missing side as sqrt (34), but that all I've got.

And this is kind of separate from this problem, but I don't really understand the Pythagorean Theorem with these problems. This one made sense, but another one I did had 40 as the hypotenus, and 41 as the opposite. I had to find "c". Well, I ended up with a=sqrt(40^2-41^2), because that makes sense, right? It turned out to be 41^2-40^2, but how? Wouldn't that have been sqrt(-41^2+40^2) if written the other way? I took a^2+b^2=c^2 and solved for "a". Is this not correct? I'm very confused, and any help would be appreciated! But the main focus of this thread is in my attachment. :) I didn't know how to write those characters so I drew up the problem.

http://img32.imageshack.us/img32/8923/mathproblem.png

Since you already got all the sides, all you need to do is plug in the numbers.

Sin = opposite/hypotenuse
Cos = adjacent/hypotenuse
Tan = opposite/adjacent

In other words "SOHCAHTOA."

Cot = inverse of Tan = opposite/adjacent
Sec = inverse of Cos = hypotenuse/adjacent
Csc = inverse of Sin = hypotenuse/opposite

Using this information, sin fishy (alpha?) would be 3/radical 34. In turn, cos B thingy would also be 3/radical 34.

Sorry, I forget the names of the thingies. Haha. I hope this helps.

Edit: For your question thingy about the Theorem, are you sure the read the problem correctly? According to the answer, 41 should be the hypotenuse.

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Originally Posted by Chinnie15

I am in need of help solving this problem. I got the missing side as sqrt (34), but that all I've got.

And this is kind of separate from this problem, but I don't really understand the Pythagorean Theorem with these problems. This one made sense, but another one I did had 40 as the hypotenus, and 41 as the opposite. I had to find "c". Well, I ended up with a=sqrt(40^2-41^2), because that makes sense, right? It turned out to be 41^2-40^2, but how? Wouldn't that have been sqrt(-41^2+40^2) if written the other way? I took a^2+b^2=c^2 and solved for "a". Is this not correct? I'm very confused, and any help would be appreciated! But the main focus of this thread is in my attachment. :) I didn't know how to write those characters so I drew up the problem.

http://img32.imageshack.us/img32/8923/mathproblem.png

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Begin by using the pythagorean theorem to find the hypotenuse. Then use the definitions of the trigonometric functions to find the indicated quantities.
Do you know these definitions?

Thanks! I know the definitions, but I'm having a hard time applying them and how to know which to use and when. Oh, I found my mistake on the one problem. It was the hypotenuse. I hate triangles, lol. They all look the same to me.

Thank you again!