Math Final

May 18, 2009 3:42 PM

Hi everymathperson! I guess I'll just jump right in: What is the radius of a circle with a subtended theta angle of 60 degrees and an arc length of 10?

I used the fact,
(arc length)/(circumference(2*pi*R)) = (Theta(60))/360


This was just on my final, and I can't wait an entire week to see the answer, I can't get anything to work that checks out, .268 or something was my best guess, thanks so much everyone who's better at math than I am.

posted by Benzle to Science & Nature (12 answers total)

Using your own formula, you should get something much closer to 10.

R = 10 * 6/(2*pi) = 60/(2*3.14) = 9.54
posted by peacheater at 3:48 PM on May 18, 2009

A sort of "hmm does this feel right" evaluation for this is that 60 degrees is the inside angle of an equilateral triangle. The arc is a little longer than the radii, so peacheater's answer seems right. .268 is clearly wrong.
posted by aubilenon at 3:52 PM on May 18, 2009

There's also the formula:
Theta (in radians) = arc length/radius.
Using your numbers, you should get:
radius = arc length/(pi/2) = 9.549
posted by derogatorysphinx at 3:52 PM on May 18, 2009

The fact you state seems to work, but I get a radically different number than you do: 9.55

(arc length) /(2*pi*R) = 60/360
Cross multiply: 120*pi*R = 360* arc length
R = 3 * arc length / pi = 9.55 (approx)

Also, arc length = radius * angle in radians
so radius = (arc length) / (angle in radians)
60 degrees = pi/3 radians
Again, radius = arc length * 3/pi = 9.55 (approx)

To do a quick mental check if your answer is in the right ballpark: the above makes sense, since the circumference of a circle is 2*pi*radius or approximately six times the radius. Since 60 degrees is one sixth of the circle and you have an arc length of 10 for that angle, the radius should be a little less than 10.
posted by wiskunde at 3:57 PM on May 18, 2009

Yep, your formula is right but your final answer is wrong. It's off by a factor of about 36, which suggests that you might have inverted the 60/360 term at some point. That is, 10/2ΠR=60/360 is the correct formula and gives R=9.55=49; 10/2ΠR=360/60 would be the wrong formula but would give you an answer of R=0.265.
posted by DevilsAdvocate at 3:57 PM on May 18, 2009

and gives R=9.55=49 9.549
posted by DevilsAdvocate at 3:58 PM on May 18, 2009

Yeah, that was supposed to be pi/3 radians, not pi/2....
posted by derogatorysphinx at 3:58 PM on May 18, 2009

your angle, say α, is π/3, the length of the arc is 10=α*r, so r is (3*10)/π or -roughly- a little less than 10 itself.

On preview, DevilsAdvocate 9.549 feels right. Sorry.

(ditch degrees, start thinking and visualizing in radiants, then convert if an answer in degrees is required).
posted by _dario at 4:09 PM on May 18, 2009

Maybe I'm making this too easy, but 60 degrees is 1/6 of the circumference, so the circumference is 60. So, the radius = 60/(2 pi), or about 9.5.
posted by monkeymadness at 5:24 PM on May 18, 2009 [3 favorites]

This boils down to why radians are a much better way of measuring angles than degrees: they allow you to turn unintelligible formulae like the one you gave to obvious calculations like monkeymadness':

"Maybe I'm making this too easy, but 60 degrees is 1/6 of the circumference, so the circumference is 60. So, the radius = 60/(2 pi), or about 9.5."

posted by katrielalex at 6:41 PM on May 18, 2009

This boils down to why radians are a much better way of measuring angles than degrees: they allow you to turn unintelligible formulae like the one you gave to obvious calculations like monkeymadness':

But monkeymadness didn't use radians in his calculation. The more important lesson is knowing when it's helpful or necessary to convert, and when it's not.
posted by abc123xyzinfinity at 7:15 PM on May 18, 2009

9.549 would be correct.

Glad this isn't in Metatalk.
posted by peewinkle at 7:20 PM on May 18, 2009