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#### Ragnarok

##### Member
Hello, I was working problems from a very old trigonometry book, Loney's Trigonometry from 1895. There appears here a problem stating:

The value of the divisions on the outer rim of a graduated circle is 5' and the distance between successive graduations is .1 inch. Find the radius of the circle.

I cannot determine what is meant exactly by a graduated circle, other than that it was a surveying instrument. I am also unsure if the 5' measurement is supposed to mean 5 inches or 5 seconds (I'm thinking the latter). Does anyone have any ideas? Thank you!

#### MarkFL

Staff member
The expression 5' refers to 5 minutes of arc, or 1/12 of a degree (since there are 60 minutes of arc in a degree). So, I would use the arc-length formula:

$$\displaystyle s=r\theta$$

You are given $s$ and $\theta$, so you can solve for $r$.

#### Ragnarok

##### Member
Ah! Okay. I should have said minutes, not seconds. I get it now. Not sure why I was confused.

Thanks!