Find the central angle of a circle with a radius of 3.2 cm, which subtends an arc 17 cm long.

Thanks for any help!

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- Jun 1st 2009, 06:05 PMlive_laugh_luv27Central angle of circle
Find the central angle of a circle with a radius of 3.2 cm, which subtends an arc 17 cm long.

Thanks for any help! - Jun 1st 2009, 06:17 PMartvandalay11
This question completely hinges on knowing the formula $\displaystyle S=r\theta$ where S is the arc length, r is the radius of the circle, and $\displaystyle \theta$ is the measure of the central angle of the circle in radians (NOT DEGREES)

So, we have S and r, and we need to find $\displaystyle \theta$

$\displaystyle 17=3.2*\theta$ so $\displaystyle \theta=\frac{17}{3.2}=5.3125$ if you want $\displaystyle \theta$ in degrees, multiply 5.3125 by $\displaystyle \frac{180}{\pi}$