# Calculating size of an object based on distance

So, say an object that is 10 feet tall is 100 feet away. If I hold up a ruler 3 feet away, then the object in the distance would correspond to about how many inches?

Tried using this guy: http://www.1728.org/angsize.htm to calculate the angle, which ends up being 5.7248 degrees

Then, if I solve for size using 5.7248 degrees at a distance of 3 feet I get 0.3, or 4.8 inches.

The thing is is that that does not seem accurate to me. Perhaps my perception of distance is off, but 4.8 inches looks more like a 10 foot tall object at 50 feet to me...?

I mean, it is a simple ratio really..

x/3 feet = 10 feet/100 feet right???

• Yes, it is just a simple ratio. – JimmyK4542 Jul 8 '14 at 4:22
• Alright, that is what I thought. Thanks. – CryptoCommander Jul 8 '14 at 5:25

Thanks to the intercept theorem this is indeed a simple ratio:

$$\frac{x}{3\,\text{feet}}=\frac{10\,\text{feet}}{100\,\text{feet}} \qquad\implies\qquad x=0.3\,\text{feet}$$

If you want to also involve the angles, you have