measure of central angle, given arc length, radius value

[Jen123]

Find the degree measure of the central angle whose intercepted arc measures 8 cm in a circle of radius 15 cm.

S=r0
0= s/r
8/15 cm
how would this be expressed in degrees

 

[skeeter]

multiply the fraction 8/15 (the central angle in radians) by 180/pi to convert the radian measure into degrees.

 

[stapel]

S=r0
0= s/r
8/15 cm
how would this be expressed in degrees

I will guess that, by "zero", you mean "theta", usally denoted "\(\displaystyle \theta\)" or "@". Also, I will assume that you are using the formula for the arc length "s" for an arc with radius r and central angle @, where the angle is measured in radians; namely, s = @r.

You have:

. . . . .@ = (arc length in cm) / (radius in cm)

Since "(cm)/(cm)" has no units in the answer, how are you arriving at an angle measure, "(8/15) cm", denominated in centimeters? :shock:

Also, you ask how to convert radians to degrees. This should have been covered in class, but you can figure out the relationship yourself: Since "once around the circle" is either 360° or else 2pi (radians), then 360° = 2pi radians. Then 180° = pi radians, and you can do the conversion by using multiplication and division.

For instance:

. . . . .45° = (45° / 1)(pi radians / 180°) = (45/180)(pi) radians = (pi / 4) radians

...and so forth.

Hope that helps!

Eliz.