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...sad thing is that I WAS using a rangefinder
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Get a USGS 1:2400 map of the area you are hunting. Get a pratractor with a 1:2400 scale. They work as dern good range finders.
Find the point on the map where the goat is. (You should already know you location). Use the protractor and you can get a dern accurate reading of the distance.
The thing about maps is they are "FLAT", meaning you can disregard any angle corrections shooting up hill or down hill.