Area of a Triangle - am I crazy?

[Hammertime]

Alright, I posted this in the wrong section before because I figured out that I was using the wrong method to try and find what I wanted/needed. So, I have a triangle with sides a, b, and c. I know that b= 1220 meters, and c= 1050 meters. That's all I know. I have to find the area of said triangle by solving parts of it. I think I have an answer, but it seems...Off. Here's what I did.

I figured first I'd find the contained angle between the two sides, A, by using this:

cos A = c/b
cos A = 1050/1220
A = cos^-1(1050/1220)
A = 30.60971101 degrees

From there I used the formula for the area of a scalene triangle; A = .5bc(sin A) and got an answer of 326 134.4623 meters squared.

So, I'm very sure I did something wrong. The question is: what? And how can I fix it?

Thanks in advance.[/tex]

 

[stapel]

Original thread here.

Note to poster: It would seem likely that, even with a change in "methods", the original reply to your question still holds; namely, "There is not unique solution to the problem as you state it!"

If there is further information regarding your question, please provide it. For instance, you say that "cos A = c/b", which is only true if you have a right triangle and b and c are the appriate sides. But you never specified such. Please reply with this other information.

Thank you.

Eliz.

 

[TchrWill]

Alright, I posted this in the wrong section before because I figured out that I was using the wrong method to try and find what I wanted/needed. So, I have a triangle with sides a, b, and c. I know that b= 1220 meters, and c= 1050 meters. That's all I know. I have to find the area of said triangle by solving parts of it. I think I have an answer, but it seems...Off. Here's what I did.

I figured first I'd find the contained angle between the two sides, A, by using this:

cos A = c/b
cos A = 1050/1220
A = cos^-1(1050/1220)
A = 30.60971101 degrees

From there I used the formula for the area of a scalene triangle; A = .5bc(sin A) and got an answer of 326 134.4623 meters squared.

So, I'm very sure I did something wrong. The question is: what? And how can I fix it?

If the triangle is a scalene triangle, cos A is not 1050/1220. If the triangle were a right triangle with side b equal to 1050 and the hypotenuse, c, equal to 1220, then cos A would be 1050/1220 and the area would be 1050(1220)/2.

In order to find the area of a triangle with sides of 1050 and 1220, you MUST have one additional piece of information. You need the third side or any one of the interior angles. Only if the triangle were a right triangle could you determine its area by assuming that the two given sides were perpendicular to one another or 1050 was one of the sides with 1220 the hypotenuse..