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Please look at the diagram:

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I know $D$, $\alpha$ and $\theta$. I also know the $a/b$ ratio of $k$. I don't know $c$. Can I find out $a$ or $b$ or $a+b$?

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    @joriki, now I see what you mean.. Ok.. good point2011-08-25

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This is a slightly different question to this one. But the answer is the same: it is not possible to determine $a$ or $b$ or $a+b$. Look at this figure:

enter image description here

We can move the red lines anywhere in the $\theta$ cone without changing $\alpha$ and $k=a/b$. But $a$ and $b$ are changed.

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    Thanks for the answer.. It is clear this is not possible.2011-08-25