# If a an arc of length 5.5 yards subtends a central angle of 0.5 radians on a circle, then the radius of the circle has length: How many yards?

Mar 14, 2018

radius $r = 11 y a r \mathrm{ds}$.

#### Explanation:

First convert the radians into degrees.
$1 r a d = \left(\frac{180}{\pi}\right) \mathrm{de} g r e e s$
$0.5 r a d = 0.5 \cdot \left(\frac{180}{\pi}\right) \mathrm{de} g r e e s = \left(\frac{90}{\pi}\right) \mathrm{de} g r e e s$
$\frac{\theta}{360} \cdot 2 \pi r =$length of an arc, where, $\theta$ is the angle subtended by the arc in degrees.
Thus, plugging in the values in the equation,
we get:
$\left(\frac{90}{\pi}\right) \cdot \frac{1}{360} \cdot 2 \cdot \pi \cdot r = 5.5$ yards
Simplify that to get:
$\left(\frac{r}{2}\right) = 5.5$ yards
$r = 5.5 \cdot 2$ yards
$= 11 y a r \mathrm{ds}$

Hope that helps!!