I had some problems with this problem myself, in evaluating Margaret's answer and figuring out one of my own. I had shared the answers I received with a hunting friend of mine. He picked Margaret's out and said that using her method, he did a few exmples that worked out right on the nose. I complained that I couldn't get her method or his method to work if you tried to consider the angle of the moveable mirror. He set me straight with this comment: "I am not mixing the mechanics of the device with the math. I am assuming that the device is designed to get the necessary angles and translate that into a reading I can look at."
See, I got stuck trying to figure out how the device actually got the necessary measurements, when in actuality, I have no idea, and am not likely to figure it out without doing some research! If you ignore the details, the math is not quite so bad, and I felt a lot better about it!
I especially liked that Margaret did some of the extra parts, particularly the part about how to make the device more accurate. The rangefinder that I was looking at when I wrote the problem sells for about $90. It's a pretty small device, and to make it more accurate would be pretty expensive - you are rotating a little mirror with your finger. That can't be that accurate! Read Margaret's answer, and plug in some numbers. If you change the angle by 4 or 5 degrees, how much does the distance change?
One thing I think Margaret should have been careful about was making too many statements about things that you aren't sure about. Her statements about how you might want to aim your rifle, and in particular the statement about the factors affecting muzzle velocity aren't right. There is a thin line between saying enough and saying too much, and you should be careful about it!
I really liked this problem. It gave me an excuse to play around with the internals of rangefinders (and learn that I don't know much but would like to learn more), and to do some "research", which amounted to browsing through some catalogs that I have!
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