In which triangle is the value of x equal to tan -1{3.1/5.2}

First, the trigonometric function for calculating the sin, cos and tan of an angle are only applied in right angles triangles. So, the first condition is that the triangle is right-angled.

Second, from the rules of trigonometry, the tan of the angle is calculated as follows:
tan (x) = length of opposite side / length of adjacent side 
Therefore, the second condition is that the length of the side opposite to the desire angle x is 3.1 units while the length of the side adjacent to the desired angle x is 5.2 units

Then, we have tan-1(3.1/5.2) = 30.8 degrees
Since the triangle is right-angled (one of the angles = 90 degrees), therefore, the third angle should be equal to 59.198 degrees

Last but not least, applying the Pythagorean theorem, the length of the hypotenuse of this triangle should be equal to sqrt((3.1)^2+(5.2)^2) =   6.05 units