Answer
$\theta_{max} = 22.3^{\circ}$
Work Step by Step
We can find the critical angle:
$\theta_c = sin^{-1}~(\frac{n_2}{n_1})$
$\theta_c = sin^{-1}~(\frac{1.48}{1.60})$
$\theta_c = 67.7^{\circ}$
We can find the maximum angle a light ray can make with the core:
$\theta_{max} = 90^{\circ}-67.7^{\circ} = 22.3^{\circ}$
