I'm stuck trying to solve an exercise regarding an image analysis.
Consider a book that measures 16 cm $\times$ 24 cm lying on a table. Let the vertices of the book be denoted by A,B,C,D and the vertices of the table be denoted by A',B',C',D' so that the line segment(AD) has length 16 cm and the line segment (AB) has length 24 cm. Place the book such that A=A' and the lines
AD and A'D' coincide AB and A'B' coincide
What are the dimensions of the table?
Hint: Construct vanishing points and use cross ratios.
My idea was this:
The plane spanned by the table is contained in the real projective plane.
We may consider the line CD which intersects the line A',B' at infinity and the line BC which intersects the line A'D' at infinity. Since we can interpret the point A=A' as 0 we get the following cross ratios:
I know that $D-0=16$ cm and $B-0=24$ cm. In order to solve the exercise I have to determine D-D' and B-B' but I do not see a way how to that since the values $cr(0,D,D',\infty)$ and $cr(0,B,B',\infty)$ are unknown. Is it possible to find these values or should I try to choose different points?
\Edit: I have added a picture which illustrates the configuration.