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Do you think this tool can cut a 1" piece trim wood off the house
While on the ladder? Using the half moon cutting wheel?

You realize that the tool cuts by oscillating. 1" is very ambiguous and so is ladder. Being 15' up is different than 6' and a 1" x 1/8" is different than 1" x 3/4".

Woodcraft (Fein) and Home Depot (Dremel) have areas where you can play with the tool. There are cordless versions too. Check out FEIN Power Tools Inc. - Electric power tools for professionals. (http://www.feinus.com) for some videos. I think the Dremel site has videos too. Harbor Freight has the lowest cost version of the tool.

The answer is likely. I own the Fein version.