Question 1210262
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Let ABC be a triangle with side lengths AB = 5, BC = 6, and AC = 9. 
What is the area of the triangle with side lengths tan(A), tan(B), and tan(C)?
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        This problem's formulation looks strange,  but I will interpret it  " as is ",

        i.e.  in a way as I read it.



<pre>
Compare  |AB|^2 + |BC|^2  with  |AC|^2.


We have  5^2 + 6^2 = 25 + 36 = 61  for  |AB|^2 + |BC|^2  and  9^2 = 81  for  |AC|^2.


Since  |AB|^2 + |BC|^2 = 61  is  less  than  |AC|^2 = 81,  we conclude that  angle  B  is obtuse.


If so, then tan(B) is negative.


The implication is that such a triangle with the sides tan(A), tan(B) and tan(C) does not exist.
</pre>

Solved.