10 foot pole, or 10 feet taller than the observer eye level?

It is ten feet to the top of the pole from ground level.

The observer is standing three feet away from the pole.

What is the height of the observer's eyes? It matters.

I do not think so and here is why.

The observer (unless he is Robert Wadlow, nearly ten feet tall) would have eyes positioned along the angle of the hypotenuse (in this case the imaginary line formed by top of the object extending to the top of the pole and then to the eye of the observer, then through to the ground).

How drastic an affect could that have?

For instance, mountain top calculation...

Peak observed from a distance of 80 feet away.

10 foot pole erected.

25 feet further away, observer can see the top of the pole and the top of the peak.

105/25 = x/10