# A circular arc of length 16 ft subtends a central angle of 25°. How do you find the radius of the circle?

Jul 4, 2016

Consider the following diagram

The formula for arc length is $s = \theta \times r$, where $r$ is the radius, $\theta$ is the center angle in radians and $s$ is the arc.

We can convert 25˚ to radians using the conversion factor $\frac{\pi}{180}$.

$\theta \text{ in radians} = 25 \times \frac{\pi}{180} = \frac{5 \pi}{36}$

Now, solving for $r$ in the formula we have $\frac{s}{\theta} = r$

$\frac{16}{\frac{5 \pi}{36}} = r$

$\frac{36 \times 16}{5 \pi} = r$

$36.67 = r$