SOLUTION: Ok got a real life problem. I'm trying to figure out what the distance of an item is. I know that item (A) is 84 inches wide. It appears to be the same size as Item (B) which I kno

Question 830516: Ok got a real life problem. I'm trying to figure out what the distance of an item is. I know that item (A) is 84 inches wide. It appears to be the same size as Item (B) which I know is 2 inches wide. Item (B) is 192 inches away from me. How far away is Item (A)? Thanks.
Answer by KMST(5347) (Show Source): You can put this solution on YOUR website!
Here is the drawing (not to scale, because with such a difference in sizes, if we see the large object at a large distance, we could not really see the small object and the small distance).
E is where your eye is.
I drew object B right in front of object A, so that B exactly hides A,
but you could also see that they appear to be the same width if one was a bit over to one side.
There are 2 similar triangles in the drawing.
For the smaller triangle, the base is 2 inches (the width of object B) and the height is 192 inches (the distance to object B).

(I could not draw it to scale, because with those measurements the triangle would be too "skinny" to see it as a triangle, and object B would look like a dot).

For the larger triangle, the base is 84 inches (the width of object A) and the height is inches (the distance to object A, which we are trying to calculate).
The larger triangle is a scaled-up version of the smaller one.
It is times larger.
The base of the larger triangle (the width of object A) is 42 times larger than the base of the small triangle (the width of object B).
The height of the larger triangle (the distance to object A) is 42 times larger than the height of the small triangle (the 192-inch distance to object B).
The distance to object A is

NOTE: Math teachers would make a lot of noise about the two triangles being similar, and the angle at E being the same for both triangles, and the lengths of sides being proportional, but you said it was a real life problem, and I tried to get as real as I could.
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