Show that the forces form a couple (algebraic)

[Kinhew93]

Homework Statement

A Triangle ABC has sides of length a, b and c labelled according to the usual convention. Forces of magnitude ka, kb and kc act along BC, CA and AB respectively, with the direction given by the order of the letters. By considering the vector sum of the forces, or otherwise, show that these forces form a couple, and find the moment of the couple in terms of the area of the triangle.

The Attempt at a Solution

Let the angles at B and C be theta and alpha respectively.

Resolving horizontally: [ka - kb.cos(alpha) - kc.cos(theta)]N
Resolving vertically: [kb.sin(alpha) -kc.sin(theta)]N

So I assume that the first step is to show that the above expressions are both equal to 0, but I'm not sure how to do that. Any tips? Is my approach correct?

Thanks :)

 

[barryj]

Sketch and label the triangle. What does each leg of the triangle represent in terms of a force. Is it obvious what they add up to?