size at a distance Can someone help me please.
If I held up my thumb at full arms length into the sky. My thumb is the width of an object I am looking at, at 2000 meters away. How big is the object in the sky?
 A: The way we do this is to consider the angle subtended by your thumb:

The angle subtended is the angle between the dashed lines. Obviously this depends on how big your thumb is and how long your arm is, but in general this angle is taken to be about $2$º. Someone actually did a study to verify this, proving mainly that some scientists have too much free time.
Anyhow, if your thumb exactly covers the distant object then the distant object also subtends two degrees, so we just need to relate the angle subtended to the size of the object.
If you are looking at an object a distance $\ell$ away and it subtends an angle $\theta$ then the size of that object $d$ is just:
$$ d = 2\ell\tan\frac{\theta}{2} $$

In this case you know $\ell$ is $2000$ metres, and from the above you know $\theta$ is two degrees, so you can calculate the size $d$.
A: As sted by John, the ratio of width d over distance l $\frac d l$ is a function of the angle.
Intercept Theorem tells you that if the angle stays the same (i.e. your thumb just covers the object) $\frac{d_1}{l_1} = \frac{d_2}{l_2}$.
If we take your thumb to be 2 cm at a distance of 1m, then the object at 2000m has a width of $d_2 = \frac{2\, \rm cm}{1\, \rm m} \cdot 2000\, \rm m = \textbf{40 m}$.
