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You could use a theodolite. But remember that the ground is not flat. So you need to measure the vertical difference in height from the base of the tree to the theodolite. And you need to measure the horizontal distance, which would require other measurements in other locations. And you need a location where you can clearly see the top of the tree. This is all a bit complicated for someone without topographic surveying experience.

A tape measure is simple and easy to do accurately. And of course they will want to climb the tree anyway.