Dangerous trees are referred in the industry as "hazard trees". Cutting down a tree is called "felling". Trimming would be "pruning" or "tree trimming".
So far as writing to a lawyer (or anyone). Basically you want to communicate what you are intending to say. A good way to do this is to not use acronyms or technical language, but to use common language which most people would understand - language like they would use in a newspaper.
Also to be more clear about what you are saying, assume the reader of your letter knows nothing about what you are writing about. So if you use a term like "hazard tree", instead include an additional description of the term after using it like this: "hazard tree" (a tree which poses danger to people or property). Or instead of just "felling", say "felling" (cutting down the tree). Then you are using the industry term and common language as well. The reader of your letter will be sure to understand what you are trying to communicate!
Here is information on hazard trees (trees which pose a danger to people or property)...
I agree....best to clearly describe what you mean. As for "tree felling", that makes me think the tree is taken down in one piece. "Tree removal" is far more familiar to me; you can add details. Large trees are taken down in pieces, larger limbs cut off first, then the main trunk in sections probably.
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