tan^-1(16/x)=90; x = ABC. Other calculators show that there are no answers possible. I would like to know why, thank you in advance.

This says that 16/x = tan(90°).  But tan(90°) is undefined.  The limit of tan(θ) as θ approaches 90° from above is -∞; the limit as θ approaches 90° from below is +∞.  

Hence there is no value of x for which tan^-1(16/x) = 90°

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It's a limiting thing, but I suppose that you could argue that x = 0 is a solution.

It is not phrased as a limiting question anon.  

And if it was it would have to be also have to be stated as "from the positive side"

Hence there is no answer.

Thank you all.

I did say ' that you could argue that '... .

If the 'function' mentioned in the question were tan, then the discontinuity at pi/2 would make it unreasonable to talk about the limit without further information as to whether we were approaching from below or above.

However, the 'function' mentioned in the question is the inverse tangent arctan. This is multivalued and if you take usual view of working within the principal range, there is no discontinuity. Asking what happens to the inverse tangent as its argument tends to infinity is quite reasonable.