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Lightning55 · Apr 18, 2009, 02:42 PM

I'm having trouble figuring out what a particular question asks for.

If you have a circle with a radius of 5 and a central angle of 2.8 (there are no units, no degrees or radians, which is what primarily confuses me), what is the arc length that is intercepted by the central angle?

Perito · Apr 18, 2009, 04:00 PM

The radius is 5 units (cm, m, in, ft, whatever), the diameter is, therefore, 2πR = 10π or about 31.42 units. The central angle is 2.8, therefore you have

$\frac {2.8}{10\pi}\,\approx\,0.0891\, units$

There are 360 degrees (2π radians) in a circle. So you can figure out the number of degrees or raidians by multiplying by one or the other

$\frac {2.8}{10\pi}(2\pi)\,=\,0.56\, radians$

$\frac {2.8}{10\pi}(360)\,\approx\,32\, degrees$

The units are irrelevant.

Lightning55 · Apr 18, 2009, 08:17 PM

Ah I see. I got the .0891 after I posted the question, but I had no idea that you could convert it like that. Thanks a lot :) It opens a new door in mathematics for me.