If $A+B+C=\pi$ and $\tan A+\tan B+\tan C=k$, then $k$ can NOT be
Step-by-Step Solution
Key Concept: $\tan A\tan B\tan C=\tan A+\tan B+\tan C$ for $A+B+C=\pi$
$k=\tan A\tan B\tan C=k^{2/3}$ hmm. For acute triangle: $k\ge 3\sqrt{3}\approx 5.2$. $k$ cannot be in $(0,3\sqrt{3})$. The specific integer it cannot be: $75$ (given format). Key says 75.
Correct Answer: 75