Consider the absolute value, because we only worry about the quadrant later.
Thus, we know that the hypotenuse has a length of 4 units, and the side opposite the angle, A is √3, because this is the nature of the sine function in relation to its triangular component.
The missing side can be found using Pythagoras' Theorem: 4² - (√3)² = x² 16 - 3 = x² 13 = x² x = √13
Since angle A is in the third quadrant, the tangent function will produce a positive angle.