MHB Calculating the Radius of a Graduated Circle

  • Thread starter Thread starter Ragnarok7
  • Start date Start date
  • Tags Tags
    Circle
AI Thread Summary
The discussion revolves around calculating the radius of a graduated circle based on a problem from Loney's Trigonometry. The key measurements include divisions on the outer rim of 5 minutes of arc and a distance of 0.1 inches between graduations. The correct interpretation of 5' is clarified as 5 minutes of arc, not inches or seconds. The arc-length formula, s = rθ, is suggested for solving the radius with the provided values. The confusion regarding terminology is acknowledged and resolved.
Ragnarok7
Messages
50
Reaction score
0
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!
 
Mathematics news on Phys.org
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:

$$s=r\theta$$

You are given $s$ and $\theta$, so you can solve for $r$. :D
 
Ah! Okay. I should have said minutes, not seconds. I get it now. Not sure why I was confused.

Thanks!
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top