Finding $\tan x$ given $\cos x=\frac34$ where $180^\circ<x<270^\circ$

Question

Given that $\cos x=\frac{3}{4}$, find $\tan x$, for $180^\circ<x<270^\circ$.

Since it is in the third quadrant, $\tan x=\tan (x-180^\circ)$. However, I am unable to continue, as I am unable to construct a triangle to solve this.

Answer 1

The way this problem is set up, it has no solution. If $180^\circ < x < 270^\circ$, so that $x$ is an angle in Quadrant III, then the cosine of $x$ must be negative, so it cannot equal $\frac34$. There must be a typo somewhere.