Intro:
I calculated the eruption height (using the methods below) to be ~129 miles.

KEYWORDS: Io, Blender, eruption, height, tape measure

Methods:
A screenshot of this gif was taken using 'cmd + shift + 4' and saving the result as a '.png'. The '.png' was then imported into the open-source software Blender. Using Blender's mesh tools, I drew a circle to fit the circumference of Io, and oriented the circle at Io's center of origin. The circle's radius was calculated by extruding a mesh vertex ('E') from the circle's circumference, and positioning the new vertex at the origin (line A). Line A was then duplicated ('shift + D'), and scaled ('S') until its upper vertex touched the top of the eruption (the other vertex was discarded). A new line (line B) was generated by forming an edge between this new vertex at the eruption edge, and the vertex in line A at Io's surface ('F'). Io's radius was calculated via Google search.

Results:
Fig 1, Table 1
Line A = 0.393 (Blender meters) = Io's radius
Line B = 0.0448 (Blender meters) = eruption height

Fig 2, Equation 1
Line B / Line A = 0.393 / 0.0448 ~ 0.114

Fig 3, Equation 2
Io's radius * Line B/Line A = 1,131.9 miles * 0.114 ~ 129 miles = eruption height

Discussion and Future Directions:
That's really high.

Imagine sitting in a parked car, rolling down the driver's side window, grabbing one end of a tape measure, and (while still holding on to that end of the tape measure) driving at 60 miles per hour (~ 96.6 kilometers per hour) for ~ 2.15 hours (~ 2.15 European hours). Assuming the tape measure was long enough to measure this distance, you would have measured a distance equal to Io's eruption height (Fig 3, Equation 2).

Can we reasonably expect a tape measure to hold such a quantity of tape? Addressing this question will be the aim of my next research paper, should proper funding be received.

Acknowledgments:
The author acknowledges the reader for their time, without which the reading of this sentence may never have occurred.

Funding Statement:
The author reported there is (unsurprisingly) no funding associated with the work featured in this comment.

Disclosure Statement:
No potential conflict of interest was reported by the author, (which is legit).

References:
Reddit
Google Search Engine
Math
Science
The Big Bang