#### Answer

29.2 in.

#### Work Step by Step

Arc length s (for central angle $\theta$):$ \quad s=r\theta$, where $\theta$ is in radians
Converting between Degrees and Radians
1. Multiply a degree measure by $\displaystyle \frac{\pi}{180}$ radian and simplify to convert to radians.
2. Multiply a radian measure by $\displaystyle \frac{180^{\mathrm{o}}}{\pi}$ and simplify to convert to degrees.
----------------
For the smaller gear, the length of the arc that turns is
$ s=r\theta$
$\theta=120^{o}$ needs to be converted to radians (case 1):
$s=r\displaystyle \cdot 120\cdot\frac{\pi}{180}=14.6\cdot 2\cdot\frac{\pi}{3}=\frac{29.2\cdot\pi}{3}$
This arc length is the same as the arc length of the larger wheel,
rotating through the angle of $60.0^{o}.$
$ s=r\theta\qquad$ ( ... solve for $r$)
$\theta = 60.0\displaystyle \cdot\frac{\pi}{180}=\frac{\pi}{3}$ radians
$\displaystyle \frac{29.2\cdot\pi}{3}=r\cdot\frac{\pi}{3}$
$r=\displaystyle \frac{29.2\cdot\pi\cdot 3}{3\cdot\pi}=$29.2
The radius of the bigger wheel is 29.2 in.