Calculating distance of two triangles given base and length of one Triangle diagram
G'day,
I'm wondering if it's possible to estimate the distance to an object knowing the distance between your eyes and the distance from your thumb to your eyes when held out in front of you. Say for example you're trying to judge the distance to a distant object, and you align your thumb with the object. You then close one eye and open the other, estimating that the "shift" was about 3 thumbs apart.
You measure your thumb 2cm wide, eyes 6.5cm apart and the length of your arm when held out from your eyes 65cm apart. Would it be possible to find the overall distance? I've added a diagram to try and illustrate what I'm getting at
Edit: Okay, we'll use the average height of a man (170cm). How would you go about this?
 A: You can but you need one extra information.
The thing is, you either know the height of the object, and with your measurements you get the distance it is from you, or you know the distance already and you discover its height.
Measuring the "thumbs" of the object is only setting up a scale. Then you need one of those two pieces of information to actually make the maths work. Because you already know you are working with congruent triangles, but even when I give you 2 triangles, if I give you all the lengths of one of them and then say "there are some units for which this side is twice as that one", unless I tell you what units I am talking about, you can't compute the sides of the other triangle. 
Another way of creating an intuiton as to why you need another piece of information. Just imagine a stock market. You have a currency $a $ that I can convert to $thumbs $. I have a currency $b $. I ask you to give me $10b $. You can't! Unless I tell you how to convert my $b $ to $thumbs $, you won't get it right. In this case, the centimeters you measured from your arm and eyes are $a $, the thumbs are the thumbs, and the other piece of information is $b$.
