Can anyone solve the following simultaneous equations?

A+B+C=360 degrees....................(1)
k^2=40^2+50^2-2(40)(50)cos(A)........(2)
k^2=30^2+50^2-2(30)(50)cos(B)........(3)
k^2=30^2+40^2-2(30)(40)cos(C)........(2)

probably, but if you have a 30-40-50 triangle use the fact that it is right-angled. then again, you probably dont have such a triangle...

The equations are used to solve a puzzle posted at

http://www.mathcad.com/library/Library content/puzzle.asp?num=15

There are other ways of solving the puzzle, but I'm just wondering how these set of equations could be solved. I tried, but it got messy or just went round and round and ended up at the same place where I started.

I then concluded that it was impossible to solve the equations.

However, when I viewed the solutions provided, one solution makes use of the same set of equations, except the steps for solving them are not shown.

I would like to take this opportunity to make a request to the web-master:

Is it possible for this site to be improved so that diagrams could be posted ? This will make presentation of ideas easier, and much more fun as more complicated and interesting questions could be discussed.

Or maybe diagrams created by using MSWords can be attached with messages posted?

LAST EDITED ON Mar-26-02 AT 07:04 AM (EST)
 
>The equations are used to solve a puzzle posted at
>
>http://www.mathcad.com/library/Library content/puzzle.asp?num=15

The link is mistyped. You can always use the Preview feature first to check the appearance and functionality of your post. You can also Edit your message within 1 hour after posting it.

>There are other ways of solving the puzzle, but I'm just
>wondering how these set of equations could be solved. I
>tried, but it got messy or just went round and round and
>ended up at the same place where I started.

This is what I would expect of a set of quadratic equations. At the bottom of the page you point to

http://www.mathcad.com/library/LibraryContent/puzzle.asp?num=15

there is a nice remark by Andras Horvath, which simplifies the solution greatly. It always makes sense to use problem specifics.

>I then concluded that it was impossible to solve the
>equations.

Why? Andras Horvath clearly solves the system in a very elegant manner.

>I would like to take this opportunity to make a request to
>the web-master:
>
>Is it possible for this site to be improved so that diagrams
>could be posted ? This will make presentation of ideas
>easier, and much more fun as more complicated and
>interesting questions could be discussed.

You can specify attachments when posting a question. Max size is 20KB.

>>The equations are used to solve a puzzle posted at
>>
>>http://www.mathcad.com/library/Library content/puzzle.asp?num=15
>
>The link is mistyped. You can always use the Preview feature
>first to check the appearance and functionality of your
>post. You can also Edit your message within 1 hour after
>posting it.

I'm sorry for the mistake.

>This is what I would expect of a set of quadratic equations.
>At the bottom of the page you point to
>
>http://www.mathcad.com/library/LibraryContent/puzzle.asp?num=15
>
>there is a nice remark by Andras Horvath, which simplifies
>the solution greatly. It always makes sense to use problem
>specifics.
>
>>I then concluded that it was impossible to solve the
>>equations.
>
>Why? Andras Horvath clearly solves the system in a very
>elegant manner.

I love Andras Horvath's solution. And I'm aware of the fact that there are other solutions to the puzzle. In fact, I've come up with one myself using a different approach. I wish I could view all the 7 solutions mentioned in the Mathcad website. However, I am unable to download and read those solutions in Mathcad format.

What I am now interested in is: how can the set of simultaneous equations be solved, if one is given only the equations, and that they are not linked to any specific problems.

Thank you for your comment.