# Calculate the distance of an object based on its size

My problem is this:

There is an object whose height is $30$cm. At some distance it looks like it is $0.5$cm high. Can I calculate the distance based on this information?

• Provided that "the some distance" is also known. – Mick Apr 18 '17 at 8:59
• ??? what do you mean? – Eyal Binehaker Apr 18 '17 at 9:04
• This question has been answered before here. – Kalzi Apr 18 '17 at 9:08
• The problem is that "looks like" is not well defined. How does something look like $0.5$cm. Does it look like an item having $0.5$cm that you hold at arms length in front of you? That you hold directly in front of one of your eyes? Do you have problems with seeing sizes? So unless you find a mathematical way to properly express the term "looks like", the answer is no, you can not. However, if you start with "looks like a object of size 0.5cm that is held exactly 1m in front of the observer...", there is indeed a way to do it. – Dirk Apr 18 '17 at 9:38

• From what you wrote, $h, d, k$ are lengths. So, $h/d$ gives you the tangent of the angle spanned by the height $h$ when you look at a distance $d$. This value is dimensionless, hence, cannot be equal to $k$. – Hoc Ngo Apr 18 '17 at 9:44