Given: \[ 52^\circ 52' 30'' = 52^\circ + 52' + 30'' \] Since \(60'' = 1'\), \[ = 52^\circ + 52' + \left(\frac{30}{60}\right)' = 52^\circ + 52' + \frac{1}{2}' = 52^\circ + \left(\frac{104 + 1}{2}\right)' = 52^\circ + \frac{105}{2}' \] Now, since \(60' = 1^\circ\), \[ = 52^\circ + \left(\frac{105}{2 \times 60}\right)^\circ = 52^\circ + \frac{7}{8}^\circ = \left(\frac{416 + 7}{8}\right)^\circ = \frac{423}{8}^\circ \] Since \(180^\circ = \pi\) radians, \[ \frac{423}{8}^\circ = \left(\frac{\pi}{180} \times \frac{423}{8}\right) \text{ radians} = \frac{47\pi}{160} \text{ radians} \] (Answer)