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Trigonometry "Graduated circle" problem

Ragnarok

Member
Jul 10, 2013
41
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

Administrator
Staff member
Feb 24, 2012
13,775
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 $r$. :D
 

Ragnarok

Member
Jul 10, 2013
41
Ah! Okay. I should have said minutes, not seconds. I get it now. Not sure why I was confused.

Thanks!